Do I need to install a grounding rod for a metal frame above ground swimming pool according to the national electric code?

No, no no.

The pool frame needs to connect to the exposed lug on the pump motor using a #8 copper soild wire.

Once the #8 wire connects the pool frame to the pump motor, it is now grounded through the insulated equipment grounding conductor that is with the feeder that serves the pump.

Any metal ladders etc, or metal, such as fencing, within 5 feet of pool must be connected with #8 solid also.

Assuming this is a typical above ground pool, with supporting legs every so often around the pool, most inpectors require this #8 Cu soild wire to run around the perimeter and atttach to eack leg using a lug, and this wire from beginning to end must be uncut.