THere isn't any minimum avoidance before you go mastery. rule of thumb is if you're wiping to boss berserk timer, or soft enrages (and you're almost the last one standing) you want more avoidance, if you're dying to boss damage and thats causing wipes you need more stam/mastery. 510 ilvl you are probably going to want gem stam/mastery and reforge to mastery after the hit/exp caps, but talk to your healers, ask them how you are to heal.
I wouldn't say go like that, you should probably be fully gemmed and enchanted and should certainly research the encounters fully before you dive in LFR. Knowledge of the encounters and personal performance are probably going to have a much larger impact on your ability to complete flex than your Ilvl, I've done a few Flexes with my 510 ilvl pally and DK and they where fine, our B-team struggles to do FLex and their tanks are both pushing 530 ilvl, witha decent team and oyu playing decently, you'll be fine, if you lay badly, you'll do badly.