I am wondering if it is a good idea to put a flash suppressor on my tikka t3 300wsm to help out with felt recoil, or does it cut down on the velocity of the ammo to much to make it worth it?

I assume by flash suppressor you are talking about a muzzle break? They do cut down on recoil, I do not know about velocity though. They GREATLY increase noise. If you use one for hunting, wear ear plugs or you will regret it.

I bought a Browning BAR 30-06 with the BOSS system, which is a muzzle break that adjusts in and out to tune the barrel for accuracy. The first time I shot a deer with it I felt like I had been at a rock concert. My ears rang for a while. I replaced the break with a solid piece and can now hear the action work and the ejected shell hit the ground below me. I will never use a muzzle break again for a hunting gun.

Exactly what ADVWannabee said, wear ear plugs if you go with a muzzle brake. I have a Marlin 1895G Guide Gun in 45-70 that is Mag-N-Ported, first time I shot it I thought I blew my right ear drum, my right ear rang for over a week. Needless to say I dont shoot it anymore, I bought a new 1895GS that is unported, it does kick harder but much more pleasurable to shoot, I can tolerate recoil better than muzzle blast.