1965 Cadillac Deville when accelerating

Sounds like Rich A/F mixture -Burning oil-do a compression or leakdown test to find out where its leaking at.

Oil leaking could be a seal, try valve cover gaskets first start at the top

burning oil could be valve stem seals or stuck oil rings, with the valve covers off you can change the valve stem seals if you know how, you need a air compressor and a valve spring compressor, I would start there