There's no way you're going to get a chemically propelled inert projectile to escape velocity, it's just not going to happen. You have two ways of doing it: Rocket-propelled projectile, or electromagnetic propulsion (i.e. rail gun).
Rocket propelled projectiles have thus far been the only successful way to launch something into orbit, via constant (and relatively slow) acceleration. A railgun could get a projectile to escape velocity, but it would take one hell of a railgun with current technology. Right now the stuff that the Navy is testing has an expected maximum velocity of ~13,000mph at the muzzle, which is roughly half escape velocity. I'm sure it's possible to rig up a one-shot discharge, and get a tiny projectile up to 26,000 or even 30,000 miles per hour, but you'd vaporize/fuse any known rail substance with that one shot.
So basically, unless you want to build an expensive railgun and have to replace the rails after every test shot to get anywhere near escape velocity, your only bet is rocket propulsion.
If you wanted to go the railgun route, though, definitely take the rig up in a plane or fire it from the top of a tall mountain, at least 10,000 feet. If you could get up to 20,000, even better, far less drag to slow down the bullet, so you'll need less initial velocity (not to mention the bullet will be subjected to far less friction heating, and thus possible vaporization itself)
