Okay,
This is an important point that I feel isn't being addressed.... But, believe me when I say that my only interest in pointing this out is to help you up your game.
First of all, as you didn't have set plans with this girl (or at least that's what I understood), you didn't REALLY get flaked on....
However, I can definitely give you the PUA theory (and it may not apply, but this is the textbook answer) for why she dodged you.
It has to do with framing, the first thing you asked this chick when you saw her was do you want to get dinner?
That's asking for a pretty high investment on her part because going out to dinner sets the serious relationship frame for most women.
Had you suggested something like her coming to join you out with your friends for a casual evening where you can build attraction and Comfort (Also, you can dhv by demonstrating some strong social proof, if you pick your friends wisely), she would be thinking "do I want to go out and have fun with this cute guy?"
But when you go straight to dinner her mind immediately has to decide whether or not she wants to DATE you and that's a high investment for someone she hasn't built the appropriate levels of attraction and comfort with (yet).
I know this seems counter intuitive, because as men we just think dinner is an opportunity to get to know each other, but to her it's "why does he want to buy me dinner, he doesn't even really know me.... he must not have many options..." (dlv) and she immediately has to consider the 'couple' frame when you suggest dinner, so she has to think "Do I want to DATE this guy?"
I have made this same mistake SOOOOOO many times in the past, so it's nothing to feel bad about. If you are really interested in her, I suggest reading a text game book and learning how to ping and build her up to a comfortable enough mentality to see you again, and then keep it casual (remember, To her you cant be looking to "date" or "sleep" with her you just have to be this cool dude that likes to hang out with people.) that'll put her guard down long enough for you to DHV and build attraction....
Remember YOU don't get rejected... you're approach does.
Modify Modify!
Hope that helps, best of luck man. If you'd like some basic text game pointers I'd be happy to oblige!