A .308 caliber brake is common on 6mm, 6.5's and 7mm cartridges. You can get caliber specific brakes if you prefer though. I don't know anything about the brake in your link but I do know cheap muzzle devices can have a negative affect on accuracy. I would stick to name brand parts if you can help it. If you are on a tight budget, I would get a thread protector until you could swing a quality brake.
I highly recommend you look at these. You can get them in the caliber you want and they don't require a gunsmith or shims to time them. Very user friendly and great performance.
https://www.americanprecisionarms.com/products-page/muzzlebrakes/gen-ii-little-bastard/If you are interested, I have a Badger Micro FTE that I will make you a good deal on.
