What causes headlights to dim and flash while driving 96 blazer?

Generally one of two things will cause headlights to dim; a power drain somewhere else (A/C compressor clutch, etc.) or a bad electrical connection.

If the dash lights dim at the same time, it's most likely an electrical draw or short circuit.

Don't automatically dismiss the A/C clutch because the A/C isn't on; some vehicles also run the A/C in defrost mode to dry the air.