Can my man take flucloxacillin for he's toothache?

No: You should never take anyone's medication other than your own. There are many reasons for this such as potential allergic reactions or drug interactions, expiration of the medication, or it might be the wrong medication. If he has a tooth ache he should see a dentist because even if the antibiotics were to help he still needs to get it looked at.

Won't cure: Antibiotics reduce severity of infection and limit spread of infection as long as you are on the Meds. Once pills are stopped, infection comes roaring back. Must have dental treatment (root canal or extraction) to "cure." Your man has to man-up and go see a Dentist who will provide appropriate treatment, including the most appropriate antibiotic. Don't self-medicate, can be dangerous.

Infection?: Antibiotics are not painkillers, so if he's infected he needs to see a dentist for care. The antibiotics will to fix the problematic tooth.