Light a candle (or anything really) inside the flask and attach the balloon, as the oxygen is consumed the pressure will decrease sucking the balloon in.
Isn't a gas produced by this reaction....so the effect is negligible?
If we're into chemical reactions...then you could always put in some ethene/ethylene and a tiny bit of chlorine...then set it out in the sun, and hope it doesn't explode because of heat. It's a gas-phase polymerization that (should) produce polyethene or polyethylene - and probably a LOT of heat, so be careful lol
I suppose too...that if you had an insulated container...you could put the flask+balloon inside of it, and then some liquid nitrogen or dry ice outside the flask, but inside the container. If the container is sealed, the stuff will evaporate and increase the pressure outside the flask...and compressing the balloon into it. Probably not enough to 'coat the inside' as you speak of though.