If Gemtech says it's legal, then it almost certainly is. That said, if you want to verify it there are many other reputable websites that give information on suppressor laws on a state-by-state basis. And you can always go to your state's official hunting laws website, though that might take a lot of searching. I know in my state there are no laws against hunting with a suppressor, which means it's just not mentioned in the state hunting laws.
As far as what suppressor your dad should use, I'd recommend a .308 can; most will work fine with a .30-06 (or any other round of similar pressure or less, and of the same or smaller diameter bullet). And I'd recommend a thread-on can if you don't plan to use it on multiple rifles; they're usually more accurate than quick-detach cans and you don't need to buy an extra muzzle device. The AAC Cyclone is a great thread-on .308 can. It's very quiet and durable; heck, it's strong enough that it's full-auto rated.
Keep in mind that many rifles don't have barrels thick enough to allow them to be threaded with the standard 5/8x24 threads, and the ones that do are too heavy for many people to want to take hunting. Most rifles with pre-threaded barrels are heavy-barreled marksman rifles and are heavy enough that I wouldn't want to lug them around on a hunting trip.
There are very few, if any, .30-06 hunting-weight rifles on the market with flared and 5/8x24 threaded muzzles, so your dad will probably have to have his rifle threaded in 1/2x28 (provided his barrel is at least 1/2 thick) and then use a 5/8x24 adaptor.
0331: "Accuracy by volume."