How quickly can a tooth infection (abscess) spread?

Depends: Dental infections can be massive and life threatening by impinging on the airway (known as ludwig's angina). They can also work their way out very slowly. It's best to resolve the cause of the infection as soon as possible to avoid emergent problems.

See a dentist ASAP : It is not healthy to have any type of infection inside your body. The infection from an abscessed tooth gets spread not only to your next tooth but it also may spread internally trough your blood stream to other parts of your body. Why wait, there is nothing to gain see a dentist asap.

Very fast: It depends on a lot of factors such as how strong your immune system is, how agressive the bacteria are, and the location of the tooth.