Looks like you need to get the brakes looked at. If there isn't enough on the brake pads it causes components to rub against each other which is essentially metal rubbing against metal which is probably the cause of your screeching sound. Its is probably one of the following. Brake rotor, Brake disc, Brake drum, or the brake rotor specs.

Good Luck!

Dear ksubilly--  I could probably give you a firm diagnosis if I could see your brakes on your 1996 Chevrolet Tahoe.  From what you describe I would guess that it might be the backing plates in your brakes which are rubbing up against the rotors.  Of course, the faster you go the more noise they will make.  The best bet for you would be to have a good mechanic look at the brakes and confirm where the rubbing is coming from.   Good luck from Bovan.