That flapper is a weir and just keeps debris caught by the skimmer from going back in the pool when the pump turns off. May also create a little better skimming action. Have you tried PVC cement? Yellow can, multi-purpose. Depending on where it broke it may not be fixable. I don't know specifically but it would seem like an easily breakable piece and should be able to be replaced easily, if you can find one.
Al