The reason people don't take flash on yuumi is because flash is primarily a positional defensive spell. Ideally on yuumi, you will never need it late game except when your team lost a team fight and your entire team died. Even early game it isn't that good because of the existence of your e, exhaust, and heal. Your e and exhaust speed up your movement speed which can help you escape, and your exhaust will make it harder for the enemy to catch you. Flash is only really considered an option in iron or bronze when your adc is constantly overextended or doesn't know how to play with a yuumi, but you are giving up so much just for a slightly better early game. Exhaust however is better for every part of the game because the slow and damage reduction can save your carries' life in a team fight, but your flash would be useless until after a team fight. In conclusion, while flash is a bit viable in the early game, it is next to useless in the late game, but exhaust gives you a bit of agency to save your carry, catch out opponents, and can still save you early game.