I live in the Keller area and have clay soil with Bermuda grass in a less than one year old house. This is a new house and the backyard bermuda is basically dead. I would like to replace the bermuda with buffalo grass. Question is:

Can I just till up the bermuda since no flower beds will go in this area and add amendments to the soil or should I kill the grass first? Also, advice on buffola suppliers and proper amendments to add.

Just depends whether you want a pure buffal grass stand. Need to start with a clean slate for that. I don't mind the mix of bermuda and buffalo.

If I was to just replace the bermuda with bermuda would I need to remove the old grass or just till it up?

You could do either if it is all completely dead. (I wish all the bermuda in my yard would die). If the bermuda is green at all, do not till it in. You should not bury anything green it will cause problems.

If you do not mind bermuda, just put out the buffalo seed. If you are planting from sod, I think it may be best to remove the bermuda.

You said the bermuda was "basically dead." With bermuda if there is one living root, you will have a bermuda grass lawn again in no time. If you want to get buffalo grass in, you need to live with that thought. It will be a mix. Unless you mow it twice a week, the bermuda will send its seed heads above the mowing height and look like bermuda gone to seed. That's a sad fact of life with bermuda. You might be able to get rid of the bermuda with a dense form of bermuda like Turffalo from Lubbock. Grow it tall and the bermuda might die out. That would be my most encouraging news. I've seen Turffalo in action and it looks great at any mowing height from 3/4 inch to 4 inches high. If you have ANY shade, it will leave bare soil.

I believe the buff seed sprouts in the summer heat. You should check with suppliers on that or maybe someone else will write in. Turffalo is only available in sod.

David is right on target there! If you have a runner that looks dead, more often than not, it is alive. Sod is always the best way to go, although it is more expensive. Starting from seed can be difficult, according to some folks. There was a thread somewhere in the discussion board about bermuda vs. buffalo. You might want to do a search for it.
By the way, yes, it does need warmth to sprout.