Jaynes analyzes coin flipping on pages 317-320 of PTTLOS. He might have more in a separate paper somewhere. Pretty sure he did, because I remember a state space and control discussion that seems similar to what you're getting at that isn't in the book.

Also, I prefer his terms of ontological and epistemological randomness. From a mechanical perspective, a coin flip will be epistemologically random if the state space is finer than your control space - i.e., the result is completely determined by the physics, but your lack of precision in controlling the flip parameters, and therefore lack of knowledge about them, makes you unable to predict the outcome.

But Jaynes goes on about how to control a flip by the method of flipping - he finds a state space where an ordinary person has sufficient precision to be able to control the outcome of the toss.

Others have done the same analysis, and confirm both the theoretical and empirical results - they can do it too.