When there is a possibility for a girl to flake on you, immediately make backup plans and stick to them if she flakes. When girls have flaked on me in the past, I went out or hung out with friends and made jokes about how women behave.
Flaking overall sucks but there are degrees to watch out for. If you agree to meet someone at a certain time, you drive 30 miles and she doesn't show up, she must be seriously messed up to pull off something like that. But if you have a date and she cancels, brush it off, go to the gym, park, concert, show, bar, anything at all to forget about it.
The reason why I don't burn bridges or react to flaking in front of women (unless the flaking resulted in major time wasting or damage) is because I have had initially women play games like that with me and eventually fell in love with me.
It will not work every time, but looking back I was doing all the right things and didn't even realize it. I showed confidence and indifference, showed interest but not desperation, showed value but did not seek approval.
Years ago this great looking girl drove me crazy and she did a lot of things to brush me off, I had a gut feeling that she liked me but was doing her best not to like me for some reason. I remained persistent and it turned to be the best relationship I've ever had. I asked her later on what happened to make her change her mind. She told me she didn't change her mind, she had always liked me but was afraid to get involved emotionally, and that she simply couldn't resist me because I seemed so genuine and most important, persistent.
Obviously this does not apply to all situation, it's our job as men to explore all opportunities. Sometime you get what you want and sometimes you don't. Doesn't mean you did something wrong or there is something wrong with you.