Is this a sustainable betting strategy on a 50/50 game? There is a 50/50 chance of winning a game. I bet small on every game and wait for a certain number of losses in a row, say 5, and then bet big (more than 32 times the original bet) on the 6th game, thus increasing the probability of success. If I still continue to lose I then double up every time until I make back that 6th bet (this would be the Martingale system). I can't see the flaw but I feel like there is one? Can anyone give a probabilistic explanation as to why this strategy would fail?

There is no problem in what you describe. But your strategy assumes that you have an unlimited "bank" to bet from.

If you have a finite amount of cash in bank, then the probability of eventual bankrupt is equal to 1.