How long will friction burn on my penis take to heal?

Depends: Depends upon the severity and whether you let it rest or send it back into action before it's had time to fully recover. Should be the same as any other bruise on any other part of your body. If it gets bigger, red or swollen, contact your doctor.

Simple Care: The good news is that area has fantastic blood supply and so healing will occur rapidly. Inflammation (red, hot, tender swelling) is the body increasing the blood flow to the injury to bring healing factors to the area and also the veins expand to carry bad stuff away. Dressings and ointments are of no value there. Avoid further trauma to the area and let nature take it's course.