If someone had chlaymidia and it got into the prostate, let's say the treatment cured the infection in the urethra but it survived in prostate, would it spread back from prostate to the urethra again?

Unlikely scenario. The antibiotic enters the blood and goes to all tissues supplied with that blood, including the prostate. The doses that cure the disease in the urethra are more than adequate to cure any that enter the prostate. Re-infections by chlamydia occur from exposure to an infected contact.

Bacterial prostatitis needs at least 3 weeks of antibiotic and some antibiotics do not infiltrate well in the prostate. If you finishes the treatment course with the appropriate antibiotic the infection is eradicated. However, with a short antibiotic course, urethritis may resolve but not the prostatitis. So the urethritis will recur when the latent bacteria in prostate cause prostatitis again.