What is the buddhist way of responding to compliments? "Hey David you're a genius!" "Hey David you look so fine!"

I think blushing and feeling a little nervous isn't really buddhist... But sometimes if you don't react this way you might look as if youre being rude

What exactly do the scriptures say of how one should respond in these situations? I've seen quotes about the Buddha saying the brahmin is "indifferent to compliments and indifferent to criticism". 

I'd like to know what the scriptures say about its possible harms, etc.  I think it is an interesting question that deserves some thought as it is part of our lives.
Just because you're Buddhist doesn't mean you can't say "thank you" :P

All facetiousness aside, Buddhism is clear about the practice.  For instance, it stresses compassion and non-attachment, so evaluate your course of action against those two.


If someone compliments you and you don't politely acknowledge the
compliment, this person may be offended.  That isn't compassionate of you.
If someone compliments you and you let it get to your head, you could
be fostering attachment towards self, the thing about which you were
complimented, and the praise of others.


So how can you approach compliments in a way that takes the above into account?  Well, you could thank the person while remembering that you are thanking them out of compassion and consideration for their feelings and not because they gave you some validation you needed.

Ultimately, it's about skillful means.  Don't seek every possible situation in Buddhist texts; rather, make sure you understand the principles and use that understanding to guide your actions.