A 30-06 is a powerful cartridge (and expensive) to learn on. I shot .22LR as a small boy for years. When I was 18 I bought a 22-250 and had no problem accurately shooting it, unless I was using some of my really crappy re-loads. I was a decent shooter, but an idiot of a reloader at 18. At 18, I had one rule which applied to everything - MORE IS BETTER (yes, even with powder dispensing).
Its hard to say if I could have picked up a more powerful rifle and learn to quickly shoot it well without having shot .22lr for years. I recon, probably not.
I was taught as a young boy to control flinching through practice and proper breathing. I went to a boy's camp for 8 summers, and twice a week all summer long we had "riflery" with .22 bolt action rifles. The counselor in charge was an ass, but he would let you know when your form was bad or when you were flinching.