My answer would be around 500fps. Again this depends on the toughnest of the "flesh" but an airgun will kill a bird at 30ft. muzzle vel is at of just under 500fps.
Just have a look at retained vel for handgun projectiles at different ranges. We know that a 9mm through to a 45ACP is lethal at 100yds. At least to people. The 45ACP is not going very fast but the bullet is heavy.
For me, my min. is 1000fps of impact vel. I know that moderate weight bullets will penetrate the lungs and chest cavity of any animal I am likely to hunt. Expansion would be very small so bullet diameter and weight become critical. Same affect as an arrow.
How fast is a 500gr 45 cal lead slug going at 500yds after launching at 1200fps? We know that will take out a buffalo. Big, bushy hide and wide chest cavity with an on the hoof weight upwards of 1500lbs.
Well, 500fps seems like a lot to me, but then again what do I know. I dropped one of my 220 grain J40 bullets from about 8 inches above my reloading table and it got stuck in the wood. I would say about 150 fps would be enough to go though a deer. (not all the way.) According to the Marines the .308 Win has to penetrate 15" of ballistic gelatin at 1000 yards so who knows. Thanks for all responces.