On average, how long does it take for an oral antibiotic for a skin infection take to take effect?

Hard to say! There are lots of different germs that can cause infections. No antibiotic helps them all. Doctors make an educated guess of which antibiotic has a good chance of working,(depending on location, health of person & symptoms of the infection), if they don't take a sample for culture, That drug may be effective, partially effective or ineffective, only time will tell. F/u if no change at all in 2-3 d.