You definitely increase your chance of a flat if you use the same tire for your trainer and for outdoor riding.

If it is an option for you I think the idea of getting a spare wheel to use on the trainer would be the best way to go since it is a pain to have to change tires each time.

I actually got a tire that was specifically designed for indoor trainer rides this year just to try it out. The tread of the tire has ridges on it that allow for better contact with the spindle on the trainer.

-traveller