Let's assume that you had your vehicle weighed and you know the four corner weight. You then divide a rear axle corner by TWO to determine the proper air pressure for each one of the dual tires. If one tire goes flat, that means that you have just doubled the amount of weight supported by the one remaining tire.
This can certainly damage that tire if driven too long in that condition.
If the exit was close(less than 5 miles in my opinion), I would drive to a safe location and park the vehicle and wait for road service. If the exit was too far away, I would move the vehicle to as safe a position as possible and wait for help.
Obviously you had to drive a short distance after the one dual blew so it might be a good idea to have the other tire removed and inspected. Another issues is that you may have to replace the blown tire with a NON-MATCHING tire so it may be a good idea to replace both of the duals.