There are 11 active judges on the DC Circuit, but one is recused. A 12th has been appointed and confirmed but his term doesn't start until September 1.
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The DC Circuit Local Rule 35(d) provides "If the en banc court divides evenly, a new judgment affirming the decision under review will be issued."
link Thus, the Court would affirm Judge Sullivan's refusal to dismiss charges against Flynn and the prosecution would continue (subject, of course, to SCOTUS review).
However, if the case is held up until September 1, I think the new Circuit Judge would be able to cast a deciding vote.
One potential outcome -- the en banc panel affirms 5-5. Later, one of the judges from the DC Circuit (Merrick Garland??) is appointed to SCOTUS, and has to recuse there. SCOTUS affirms 4-4. The prosecution would survive by the skin of its teeth at every level.