Ugh, hamstring, groin, and hip flexor pulls are the worst. Not sure how old you are, but we typically get less, not more, flexible as we age. However, you can always improve flexibility if you work at it. Yoga is a great way to increase flexibility, balance, and core strength. I know macho men will laugh, but it works.
I'm 48, wrestled in high school and am fortunate to have been pretty flexible my whole life. I'm 6'1 and 225, but I can easily squat way below parallel when back and front squatting. That's all to say I think flexibility is somewhat genetic. My college roomate was pretty tight like you described, but a phenomenal and explsovie football player.
Unfotrtunately, the only way to rehab a chronic hamstring injury is with rest, and that is gonna be tough with hunting season just starting. My daughter is a top 5 nationally ranked Olympic weightlifter, and she experienced a bad hamstring pull/tear a couple years ago. Hers went way up high under her glute at the attachment point. Even with 2x weekly rehab, electric stim, ice, heat, you name the therapy, she couldn't compete anywhere near 100%. Professional athletes with bad hamstring pulls are often sidelined on full lower body rest for up to 6 weeks.
At this point, with a busy season coming up, you're probably just gonna have to pop ibuprofen like candy and keep some penetrex or aspercreme stick handy to get by. You can always rest in the off season right?