The concept of plane fits with flat earth theory. Do you think Deleuze was a flat earther?
Here are a few qotes of Deleuze's explaning his concept of a plane: "Transcendence, vertical Being, imperial State in the sky or on earth, is religion; Philosophy is immanence...a plane of consistency between content and expression on which the absolute earth is liberated from its relative and partial strata." Gilles Deleuze
"[A] plane of consistency between content and expression on which the absolute earth is liberated from its relative and partial strata." Gilles Deleuze
"[A] plane of immanence that constitutes the absolute ground of philosophy, its earth or deterritorialization." Gilles Deleuze
"We call this plane, which knows only longitudes and latitudes, speeds and haecceities, the plane of consistency or composition (as opposed to a plan(e) of organization or development)." Gilles Deleuze
"Thus all real distinctions (mind and body, God and matter, interiority and exteriority, etc.) are collapsed or flattened into an even consistency or plane, namely immanence itself, that is, immanence without opposition." Gilles Deleuze
And maybe Latour is also, referring to what Bruno Latour means when he says, "The globe is not actually something which has any existence." at 46:59 https://t.co/CVgYmUHxsi and, "the destruction of the image of the globe" 
Also relevant is Peter Sloterdijk's explanation of why the globe became dominant and how space adventure is an impossible fantasy.
"If one had to pinpoint the dominant motif in the metaphysical era of European thought in a single word, it could only be "globalization." The affair between occidental reason and the world-whole unfolded and exhausted itself in the sign of the geometrically perfect round form, which we still label with the Greek "sphere," and even more widely the Roman "globe." It was the early European metaphysicians, mathematicians and cosmologists who forced onto mortals their fateful new definition: orb-creating and orb-inhabiting animals. Globalization began as the geometrization of the immeasurable." Peter Sloterdijk, Spheres Volume 2: Globes, p.45 (1999, tr. 2014)
"The delusions [to] seek something outside...space travel ideologies...remain unstable, shakeable autohypnotic projects against a background of futility...
The Modern Age view from the outside results not from a transcendence of the noetic soul into the extra- and supra-terrestrial, but rather from the development of the physical-technical, aero- and astronomical imagination (whose literary and cartographical manifestations, furthermore, were always ahead of the technological ones). Modern notions of flying replaced medieval ones of "ascending"; the airport earth ( where one starts and lands) replaced the ascension earth (from which one propels oneself and never returns)." Peter Sloterdijk, Spheres Volume 2: Globes (1999 tr.2014) pages 777-779