Hey Golden,
I’m not sure about the rental scene at the Grand Canyon, but if you are going to go through Flagstaff there are many options for quality bike rentals. I want to say the drive is about 1.5 to 2 hours to the canyon from Flag. There is a bike path you could take from Flag to the Grand Canyon too, but it adds a day and a half each way. Absolute Bikes in Flag is a pretty good place to start if you can’t find anything closer.