Go to your local bike shop, they'll be able to help.
If it's just flat dirt you should be fine. However if it's dirt with a lot of small rocks, chances are hwen you turn you'll fly off, and if it's big bumps, you're gunna fall off or damage your engine.I have heard that full kevlar tires resist punctures and you can get extra thick tubes.
Mind reader, Why shouldn't anyone leave the road? Just curious why you said that.
Go to your local bike shop, they'll be able to help.
Anyway, you shouldn't get to many flats, because you shouldn't be leaving the road.