What was the plan if the flight controller received a no-go prior to Apollo 8's traverse of the far side of the Moon? How would they have returned to Earth without the gravity assist from the Moon?
Apollo 8 was on a free-return trajectory when approaching the moon. If there was a no-go for the lunar orbit insertion, or if the engine failed to fire, they would have returned to Earth needing only minor course correction (doable with the RCS thrusters, which had a terrific amount of redundancy) to get home.
During the translunar coast, the large Service Propulsion System (SPS) engine in the service module would be test-fired for a few seconds. If it refused to work, the astronauts could still be brought home safely, thanks to a safety feature built into Apollo 8’s trajectory design. Known as the “free return,” it would allow the crew to essentially loop around the Moon and use its gravitational influence to slingshot them back to Earth without using the SPS. In fact, if Borman, Lovell, and Anders did find themselves with a useless engine, they would only need to perform a couple of mid-course correction burns, using the service module’s thruster quads, to keep them on track for home.
Your question is a bit confused, though: the free return trajectory is a gravity assist trajectory, using the moon's gravity to sling the ship back towards Earth. It's simply set up long before the ship reaches the moon.
This page has a nice animation of the trajectory - after the ship leaves Earth, gravity is doing all the work. The Apollo missions after 11 switched to a different profile, starting with a free return trajectory falling well short of the moon, then switching to a non-free-return with a midcourse correction.