When I say this I am NOT bashing you for buying a Marlin...I happen to like Marlin firearms.
That said...thats just another reason why I chose the Winchester Model 70...its heavier, mine is 8.75 lbs. fully loaded and ready to hunt....scope, sling, everything...a heavier rifle dampens the recoil (slows it down)
With the factory stock and pad on my M70...I can comfortably fire about 20 rounds (my reloads, pretty warm, 168's @ 2,850 fps). I have a new stock ordered and its fitted with a much better pad (Limbsaver)...you can buy Limbsaver pads that slip over the stock, they ain't very pretty...but they do work...my wife has one on her 270 (pic below)
You could also add a little weight to your rifle by putting it in a laminated wood stock...might just make it a bit more accurate too.
The right "grip" on a rifle varies a little from person to person...but practice makes perfect. You can buy reduced recoil ammo for the 30-06, try that until you get your form figured out.
To get rid of the flinch...nothing beats a good 22 rifle...LOTS and LOTS of 22 rifle...it takes a lot longer to lose a flinch than it does to gain one.