See, what is Khan Academy really lacking at this point? Is the hard part their website with youtube hosted videos? Are they really just jonesing for some mobile developers? Or is producing quality content with broad coverage and depth their bottleneck?
Making an app is the easy part. Education is not failing for want of an app. Certainly not for want of a gamified app.
But hey, I can't stop you. Knock yourself out. Hell, pitch it to YC; I hear they are doing non-profits now.