In Pokemon FireRed where is the card key?

You're thinking of the Secret Key, not a "Card Key". It's found in Pokemon Ruby and Sapphire, not FireRed.

Here's where to find the Secret Key in Ruby and Sapphire:

* Route 119 (after defeating Team Aqua/Magma in the Weather Institute): The Secret Key is hidden within the entrance to the Seafloor Cavern. Look for a small, glowing patch of ground near the cave entrance. Interact with it to obtain the key.

Let me know if you have any other Pokemon questions!