Your not touching the gas at all when u start it r u? My Rx-7 has flooded on me b4 - but i wasn't hitting the gas. After i conquer my idling problem - i'll try to figure it out.
As far as the beeping goes - i don't think i've heard it in mine. I'm not sure what it means but i will ask my friend ( he reads about Rx's and seems to find a solution to all the problems )

So once again, make sure your not hitting the gas - cuz that will flood the car. OOOOOO i almost forgot! When i get to wherever i'm going, and i park, I have to let the car sit - befor i shut it off. Your pump might be getting a lot of fuel through and if u don't let the car sit and burn it out - it might flood on you.
Don't hold me to that though. But i do know that when i put the car in park - i have to let it sit for a minute or so - or else i might flood when i try to start it again. I hope i was a help. ttyl.