The page is question is https://apps.facebook.com/gentlemensbet/ The 'Begin Betting' button won't load the oauth screen for anyone.
However, if you open it in a new window, it seems to work just fine. I can't find any reasonable explanation for this behavior and don't know how to correct this.
Add
target="_blank"
ortarget="_top"
to your anchor tag. You are trying to load a facebook URL in an iframe within a facebook page. That isn't permitted.is the error logged in the console. It is a preventive measure against click-jacking.
Your link should be: