How long does it take to blink a million times?

The normal blinking rate varies greatly between people so it is difficult to answer the question in terms of normal blinks.

If you try to blink rapidly, the muscles that control the blink will tire quite rapidly and the blink rate will drop dramatically. So again it is difficult to say.

If you manage an average of 1 blink per second, then it will take just under 11.6 days - non-stop. Your eyes may get damaged in the process.