Graphic card recomondation for flash games

No it will not improve either of these, Both are determined by your broadband speed, Just call up your ISP and ask for a unlimited upload/download speed plan.

If you plan on playing other games in future specify the max resolution of your monitor or its model number and a price range you can afford.

+1^
An on-board card suffices for your works, consider discrete cards only if you play 3D games.

Proper 3D too, not 'Runescape' etc. Your onboard would probably even support WoW at lowered settings quite well.

Your processor's speed can also severely bottleneck flash games. We have a 15Mbps connection and my wife's netbook with the Atom N270 will only play farmville at about 2 or 3 frames per second while my i3 plays it flawlessly. My brother in law's Pentium Dual Core E2220 runs it okay, but it is still kinda choppy and his video card is better than mine. This is all on the same internet connection by the way.

Flash is supposed to be 3D-accelerated now, although I'm inclined to agree with Andon48 about your processor. The novelty wore off some months ago and I blocked Farmville (didn't need to see everyone's updates), but if clicking the little eyeball icon for lowered graphic settings makes a difference for you, a GPU upgrade may help some. A GDDR5 version of the HD5550 will run around $70. For only $10 more though, you can get a much stronger HD5670. Your CPU will bottleneck it in some titles, but not too severely and a CPU overclock may help.

Hmmmm..... I didn't know the video card made much of a difference in flash. I wanted to get my wife a laptop with an i3 using the on die graphics specifically so she could use it for the Facebook games. Do you think it would run good? (Sorry to hijack the thread but I just thought of this).

A GPU upgrade will definitely not help.

It should be more than fine.

Well, I could see a difference between my dual core laptop with a X1300 GPU, a 720BE with a HD4670, and a Q9450 with a HD4850. I don't think it was all CPU.
This "might" be useful: http://www.newgrounds.com/portal/view/465908