Well have I discovered the solution for you! Using little more than my expired Duane Reade savings card, I was able to get my games to load each and every time. Follows are instructions on how I managed to fix the NES flashing screen problem.
Step 2: Remove your expired savings card
Step 4: Wedge
Step 5: Turn on the Nintendo
Take a moment to think of all the good times that are yet to be thanks to your expired savings card.