It's a trial and error process for flashing paper and is something that you could do with an enlarger with no neg in the carrier. Stop down your lens and make a test print on the paper you are going to use and do like you would do for a regular test print while printing a neg. then process in paper dev and stop/fix as normal and then look for the time when the paper just starts to show a tone/fog. Then back off to the previous expsoure that gave you that tone. you have now pushed the papers response just up to the inertia point. Then you can use as you normally would in your pinhole camera.
Your mileage may vary, but it's a starting point at least. If you find your resulting work still looks muddy, then continue to back off on the flashing expsoure until you get the tones and density you want.
Long term, I would invest in a RH designs paper flasher that can be mounted to your enlarger next to the lens stage and flash your paper that way.