Can a flat bed towing service tow a 13 ft camper

Flat bed or roll back?
Roll backs have short bed areas and the trailer must fit with the tongue to rear wheels on the bed and can hang over rear. Some towing services will not do this.
A flat bed is a tractor trailer type set up and can haul nearly every type of rig with no problem.
AAA normally does not have flat bed setups they have roll backs. They contract that to heavy towing companies. These are normally for commercial "recoveries".