My gut feeling tells me this spring would create the same result every time, because the initial conditions are the same. Unless the spring tension varies, in that case the spring tension becomes your random and you need to make sure there's no bias in it. Or the way you load the coin into the machine.
Just for fun: here's a
Machine Flips a Coin 10,000 Times.
Wouldn't the coin itself a factor to this too? Especially if you're not using the same coin to do the same flip on the machine and another factor is the atmosphere of the surrounding area and the hardness of the surface where the coin is going to land, the air resistance is always neglected in theory but in practical application, that's always considered right? And regarding the hardness of the surface, there's also the small grooves if the surface isn't smooth. Am I pedantic over this stuff or those can be considered a factor to the fairness of the flip?