What are the chances that is the cause of your flinch?I’d agree if it were just the 30-06. But I grew up shooting a 25-06 that was around 6lbs. Never had any pain. Many of the hunters in the area switched to the 25 for that reason. Much less felt recoil than the 30-06.
IMO with something like a 25-06, you shouldn’t be experiencing miserable conditions on your shoulder after 10 rounds if you are setting up on the gun properly.