Being provably fair means that the game operator cannot manipulate the outcome of your game rounds. Essentially, regardless of your bet amount, the result of any given game is going to be the same. You can verify all of your games using cryptographically secure algorithms and tools.
flashflip uses a keyed-hashing for message authentication (HMAC) algorithm to generate your rolls using three things: the daily server seed, your client seed, and your game nonce. Your client seed is unique to you (which ensures that your chain of games can't be played by anyone else). The daily server seed is the same for everyone (which ensures that the game is fair and the rolls can't be manipulated, since the server seed is revealed at the end of each day). The house edge can be verified by checking your personal chain using a local script and running it for as long as you want to (the generated games will be real).
Click here to access a PyFiddle game verifier which can be used to generate your chain of games. Use the nonce argument to define what range of games you want to generate. You can also see future games (what "could have happened") for your client seed at the time, and you can figure out median values and house edges for all games. You can also copy the script and run it locally if you prefer.