Hi /u/BluebellsMcGee!
In order to answer this question, we have to remember that acceleration in space is indistinguishable from standing still on the surface of a planet. That is, if you are in a windowless room, there is no experiment you could perform that will tell you whether you are in an accelerating spacecraft or at rest on the ground of a planet.
As a consequence, when a spacecraft is burning, the conditions on the craft are equivalent to standing upright on a (rather large) planet. Therefore, the flag will be drawn towards the rear of the craft, as it would be on a planet.
If the spacecraft is not burning, no external forces are acting on on it, thus the flag will be force-free as and will not be drawn in any direction.
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