I would agree with @Crownan here. MTB tires on a non-direct drive trainer will just be loud and inconsistent AND will destroy a very nice/expensive tire. If you want to train with your MTB on the trainer, picking up a slick tire is the best bet. I have personally used the following tire on my MTB for local computrainer classes in the past and it was great!
https://www.jensonusa.com/WTB-Thickslick-29-X-21-Deluxe-Tire
As for Flats on the trainer, you absolutely can but we recommend being clipped in just for the efficiency of it on the trainer.