How many miles can you usually put on a 97 Chevy Z71 350 Vortec?

I can't answer specifically for the 97, but my 94 had a little over 200,000 when some airhead tagged it. His insurance refused to repair it and I had to go out and get something else.

With that many miles it still didn't use oil, didn't leak and had effectively no blowby.

It's all about the maintenance. Use a good quality synthetic oil, keep it clean and make sure all of the fluids are ALWAYS up and the engine should last a long time. The vortec is effectively the same as the earlier V8's, the primary difference is the heads.