For a cheap flush (and I also recommend this as snobuilder mentioned), use cheap automatic trans fluid. Put it in and go for a ride, then drain it. After flushed out you can use a synthetic trans fluid for a cheaper solution or go with an actual synthetic chaincase lube. I used synthetic trans fluid for years with no issues.
I have had issues with my Polaris sleds when I tried running synthetic blend 75-90 gear lube. It's too thick and causes excess stress on the 5/16" bolt that holds the lower gear on and can (and has for me more than once) break the bolt. Then you have a grenade floating around in there that can destroy the chain and/or chaincase (also happened to me more than once).