What type of infection can occur from an open burn being in contact with a stray dog?

Burn infection: Burns can become infected, just as any other wound can become infected. Contact with dogs' mouths can lead to pasteurella infection. Most open wound infections are caused by more than one type of bacteria, though. If you think yours is infected, please see a doctor.

If you r healthy: Probably nothing will happen if you washed the area with soap and water and are healthy otherwise.

Depends : Burns are notorious for getting psedomonas infections which can be treated with silvadene (silver sulfadiazine) cream.. It is hard to say what you can pick up from a stray dog because it depends on the bacterial pathogens it has been exposed to.