Doxycycline dosage for 8 year old boy's tooth infection?

Antibiotics are prescription medicines. That means that they should only be sold to the public on production of a doctors authority. This authority will specify what the dosage should be for the patient and how often the drug should be administered. The reason for this is that antibiotics can cause allergic reactions that can be fatal and inappropriate or unnecessary use of antibiotics will cause resistant strains of germs to evolve which means that antibiotics will eventually stop being effective.

As you are asking what the correct dose for your child's tooth infection is, I can only assume that you have not been prescribed this medicine by a suitably qualified medic (a doctor or dentist). If this is the case you should not administer the treatment, you should take your child to see a dentist and follow what the dentist tells you to do.