ar-15
1 in 16"
The "rate of twist on rifling" is caliber specific. To give you an answer we would need to know which cartridge the rifle is chambered for.
The Remington Model 66 is chambered for the .22 long rifle cartridge. The most common twist rate for the .22 long rifle is one full turn in sixteen inches (1:16).
Your Winchester model 70 bolt action rifle that is chambered in .300 Win Mag,has a twist rate of 1 in 10.
1- 12 twist
You want a 1 in 12" or 1 in 11" twist. The twist is not only important for accuracy and stabilization of the bullet, a faster twist decreases velocity and increases pressures (which is bad). You also want a barrel that is chambered SAAMI "Spec II" or in other words has chambered with a .100" freebore or throat. The freebore is required to have a reliable, accurate rifle that functions at safe chamber pressures and allows safe use of most commercially available ammunition. There are a lot of manufacturers still selling "Spec I" 1/9 or 1/10 twist barrels, be careful.
You will have to call Remington with the serial number.
The Springfield 1903 has a 1" in 10" twist rate. The later M1 service rifle also has a 1" in 10" twist rate.
If it's an older gun it's likely 1:14 twist. Most of them were.
Please go to Customer service at Browning.com
1-in-66" barrel twist is a Kentucky rifle, not a Hawken. The Hawken brothers used a lot faster twist than that; you needed it for the prairies. Googling "Kentucky Rifle kits" will give you several makers of these rifles in kit form. As to legality for hunting? Any muzzle loading rifle that's at least 50 caliber is legal to hunt with in Idaho.
You need to see a gunsmith.