No, you can't run flash and it's probably because of the hardware restraints of the handset (I posted some of my findings about the p350 on the previous thread, but as a newbie I can't post links yet).
Nevertheless, you can watch youtube videos and play some pretty heavy games on it. It's a simple, budget handset and I find it somewhat *braver* than other budget Androids I saw in the same category. Don't give up on it.