I have a particular hitting partner who usually plays with newer tennis balls, but on days where we are stuck with mixed condition balls he doesn't seem aware enough to make adjustments. So when I see the flat (and usually darker) ball I push him back with topspin groundstroke and then follow up with drop shots or low slices
and it gets him most of the time. lol. You could probably give your opponent the same kind of troubles.
Seriously though, if you hate flat balls just bring a can of new ones next time and proceed to pop it open, when he says "I don't like playing with ____" reply with "Well I don't like playing with flat balls" the least you could get away with is mixing the old and new ones so at least half aren't flat. Then just don't use the old ones when you can help it, like when its your turn to serve.