If memory serves, the 737 had a bit of a 'history' of flameouts for a while (I think, with early CFM-56s, but excuse me if I'm wrong), and there are a few things about the way it's operated that hark back to that (the original problem relating to too low an idle in flight plus heavy rain - again, vague memories only).
Practically speaking, any time that I put the start switches ON for an emergency descent or heavy weather, they went straight to FLT, for just the reasons mentioned by downwind.
Must say that the flameout seems unlikely, but think about why you might be doing the emergency descent in the first place... If it's to do with a bleed-related problem, then you might want to be cautious.