actually, I think the original poster meant that the character is in its "idle" animation and the eyes are blinking, just as a cartoon character would do
the response about the "invincibility" is referring to "flashing" of a character who just comes back from the dead, and is usually flashing to indicate temporary invincibility, which also allows the person to get in position without being killed immediately after coming right back.
anyway... the "idle" animation is demonstrated in the "Platformer Starter Kit" that comes for free with the XNA GS.
Well, the "idle" position is only 1x1 single-frame sprite sheet, so it does not really animate, but the game code has plenty of other animations for run, jump, die, etc. so you'll get the idea.
Just replace the 1x1 sheet with a 1x4 sheet that contains a few more frames to show the blinking.
Hope that helps.