Oh boy... Here we go, Steemiacs!
With awe, I watched this particular youtube video, shared by 
I couldn't stop pondering about the science of a farted flame which burns a bypasser cat's hair, and while doing that I certainly let out one or two farts myself... I am digressing. Anyhow.
I greatly appreciate
Pixabay
Ad 's calculation
's calculation- 26.25 ml of Methane (CH4) are equivalent to 0.0017 mol and an energy release of 0.94 kJ.
- 78.75 ml of Hydrogen (H2) are equivalent to 0.0035 mol and an energy release of 1.70 kJ.
- The net energy release from burning a fart with an estimaed volume of 375 ml and a proportion of 7% of methane and 21% of hydrogen leads to an energy release of 2.64 kJ.
- So what?
The molar amount of a portion of gas can be calculated from the volume of this portion by using the molar volume of an ideal gas. The figure of the molar volume of an ideal gas was determined by Avogadro to be 22.4 L/mol at standard conditions (around 20deg Celsius and atmospheric pressure).
The formula of the relationsship between molar volume, volume and amount is:
Vmol = V / n
where Vmol is the molar volume; V is the volume; n is the amount of substance or gas
Solving the equation for n, we get:
n = V / Vmol
Now we insert the known values V = 26.25 ml = 0.02625 L and Vmol = 22.4 L/mol and get:
n = 0.02625 L / 22.4 (L/mol) = 0.00117 mol = 1.17 mmol
The combustion of methane results in a reaction enthalpy of -802.3 kJ/mol.
Therefore, the released heat energy of burning 1.17 mmol of methane is ΔH(CH4) = [0.00117 mol*(-802.3 kJ/mol)] = -0.94 kJ.
Using the equivalent calculations as in 1., we obtain the values
n = 0.007875 L / 22.4 (L/mol) = 0.0035 mol = 3.5 mmol
for the amount of hydrogen in a fart
and an energy release of ΔH(H2) = [0.0035 mol*(-483.6 kJ/mol)] = -1.70 kJ.
This one is a non-brainer. To obtain the total energy release from the fart combustion, we need to add up the enthalpies form both reactions
ΔH(total) = ΔH(CH4) + ΔH(H2) = (-0.94 kJ) + (-1.70 kJ) = -2.64 kJ
The negative prefix means that energy is released and not consumed, by the way.
Now, the question is whether an energy release of 2.64 kJ would be enough to produce a flame that burns hair. Honestly, I do not know. I do not believe so. It would produce a neat puff at best, would be my guess. As
However, we have to consider, that the lighter flame acts as a catalysator of the reaction between the fart gases and air oxygen and the chemical reaction is almost instantaneous. That means the energy released per unit of time is a large figure.
In addition, due to the direction of the fart air flow and its velocity, the released energy is propelled towards the table and simultaenously, the unlucky cat. Thus, the local temperature of the air in the immediate vicinity of the appearing cat, can be increased at least by a magnitude higher than 2.16 Kelvin for a very short time window.
These are just my considerations and we seriously need a pyrochemist here, because I cannot wrap my mind around how flames actually work.
BUT, I will show you now, why fart fire is, nevertheless, in the very close realm of possibilites when taking into account two more facts.
Have you ever tried to breathe from the back end? The carreer of a flatulist
No lengthy explanations here. There was this guy, born in the 19th century, Joseph Pujol, who, by accident, discovered that he could perform an enema on himself when swimming in the sea.
Yes, he could let his rectum fill itself with water at will. Needless to say, some time later he tried this neat trick with air and found himself mesmerized by his incredible ability to let out farts whenever and how often he wanted. He perfected his talents until he could fart melodies and imitate animals. He came to be known as Le Pétomane, becoming a top performing artist (erm, flatulist) at Mouline Rouge in Paris. Those were the days...
Le Pétomane in all his glory. Source: Public Domain.
Joseph Pujol was not a singular accident in the history of human anatomy. Even in our days, men of great valour come out and perform fart arts, as can be seen in this video that 
How can this be? Well, it seems to be that some people (including one of my friends) acquire the ability to control their anal sphincter in a sophisticated manner, opening it and by applying the right abdominal pressure at the same time, sucking in air, and closing it again; and then releasing the accumulated air in one go - the fart.
Alright... Farting at will.
The fire breathers
You've certainly heard of fire breathers, often gathering at medieval markets and performing their stunts. Some bands, like Kiss or Subway to Sally, even implement this art during their stage shows. Although this is an extremely dangerous activity (DO NOT TRY TO REPEAT THIS AT HOME) that requires education and training, some people like to experiment with simple tools like a cigarette lighter. Look at this guy:
If you ask me, that's an impressive flame! Quite similar to that, seen in the "Fart Fire - Burn Cat" video
What's actually in a cigarette lighter?
A usual cigarette lighter contains the substance butane (or propane or a mixture of both, but we stick to butane for simplicity). At normal conditions butane is a gas. That's why the cigarette lighter contains a pressurized space to keep the butane liquid. Upon release of the lighter valve, the liquidified butane starts to evoporate because the air pressure is equilibrating between outside and inside.
Pixabay
According to this site, the maximum gaseous volume of butane that can be released by a lighter is about 1.3 L or 0.057 mol. With the reaction enthalpy being -2657 kJ/mol (equivalent calculation as in the first section; consider a standard formation enthalpy of butane –125.6 kJ/mol), this would yield a total energy release per burned butane content of a lighter of -151.5 kJ.
My suggestion to explain the video - breathe in butane from the back end, spit fire to scorch the cat
Now, we have an opportunity for a relative comparison. Burning a fart at once gives you 2.64 kJ of heat energy. Burning the complete content of a cigarette lighter 151.5 kJ. That's a 57.4-fold difference. I think, we can agree, that igniting the whole content of a cigarette lighter might produce a much larger flame than seen in the "Fart Fire - Burn Cat" video.
Therefore, from the facts laid out above, I suggest, that this newly discovered performance artist, breathed in a good amount of butane from the cigarette lighter through the anus into his rectum. According to this source, someone who has mastered voluntary farting can "butthale" up to 3 liters of air.
Perhaps, a far more pleasant way to imagine what butthaling looks like. Pixabay
Let's stay modest here and assume that the guy butthaled half a litre of gas consisting of 50% of normal air and 50% of lighter butane. That corresponds to 250 ml of butane, which is roughly 0.011 mol and corresponds to an energy release of 29.1 kJ upon complete combustion. That is eleven times more than the combustion of a natural fart!
I hope you can see the connection now and that I could convince you, that it is very well possible to fart flames equivalent to fire breathing, when a flammable gas like butane is butthaled into the rectum, before it is again released and passed through a burning flame that acts as a combustion catalysator!
Such a skillful mastery has, of course, to be documented on video. That is why I am not surprised that there was a camera man filming. A final question remains, though. How the hell did the cat get in the way?A cat approximated by a quantum particle
To solve the remaining question of how likely it is, that a cat would rush through the target field of a fart fire at the very moment of its release, is beyond my expertise. However, I would like to assume that cats can be approximated by quantum particles since it is known that a cat can be everywhere at any time.
Pixabay
Theoretically, the probability of a quantum particle, like an electron, being at a particular location at any given time, can be calculated. Thus, a similar calculation should be feasible on cats.
Perhaps, 
References:
https://steemit.com/dtube/@trumpman/xesy7dvzhttps://steemit.com/science/@kryzsec/a-more-detailed-response-to-trumpman
https://www.chemistryworld.com/news/explainer-the-chemistry-of-farts/2500168.article
https://en.wikipedia.org/wiki/Molar_volume
https://en.wikipedia.org/wiki/Density_of_air
http://www.slate.com/articles/health_and_science/medical_examiner/2017/07/farting_lessons_from_flatulence_artists_joseph_pujol.html
https://en.wikipedia.org/wiki/Le_Pétomane
https://en.wikipedia.org/wiki/Fire_breathing
http://www.inpharmix.com/jps/Fuel%20Meter%20From%20A%20Disposable%20Butane%20Lighter.html
https://www.quora.com/What-is-the-liquid-contained-in-disposable-lighters-and-approximately-how-long-will-it-continuously-burn-before-running-out-assuming-I-could-hold-the-button-down-that-long
https://en.wikipedia.org/wiki/Butane_(data_page)