I made a braided table runner with sawtooth edges (not prairie points) that I did bias binding on. Talk about lots of sharp inner corners! What you have to do to get it to lay flat is to create a mitered type corner at each spot where it dips in. So you have the binding make a sharp point at the extreme inner edge, then create a fold that takes up the slack as it gets to the edge of the binding (point fold one way on front and opposite way on back of binding). It is not particularly difficult to do, but is time consuming, as it really needs to be done by hand for best results.
Yours will be beautiful!