You will See when you go into Market and search for flash you will download Adobe showcase and then it will try to get the new adobe flash 10.1 but it can not find it in market. Well at the moment Google has not fixed that but they will soon. Until then you will need to use this Beta Adobe Flash that works 100% on 2.2 update (I have it on my phone and it works ) .
Download Instructions:
Click here to download Megaupload Link
Just download it on your PC. Connect your USB to your Comp and Phone and place the download file into your phone. Then install and Enjoy adobe Flash 10.1 Beta
Enjoy
Thanks Tugdaturtle