Are there any good meat markets near Shreveport?

Really not sure if there is anywhere to find deer/elk.

Whole Foods is open now and I'm sure they have lamb/buffalo/quail/etc.

You can find lamb at Kroger, Sams, etc. Even Wal-Mart. It used to be hard to find around here except for Sam's and around Easter, but most big stores now have it all the time. Sam's has racks and deboned legs that are the best bargain. Kroger carries ground lamb at about the same price as beef. Brookshires has lamb but is high as hell on it.

I've seen frozen quail at Kroger and Maxwell's. The latter may also have some game meat in the freezer near the front.

I think I saw some grass fed beef at the new Kroger on Ellerbe the other day, but I didn't really pay attention to it.

Then you have the Farmer's Market vendors like Mahaffey Farms and Shady Grove Ranch. Those two may be the best place to look for grass fed beef. They both list it on their sites.