Should a guy be cocky-funny with a girl that's really self centered? Or should he just feed into her ego and shower her with compliments?

No.

Do NOT feed her ego!

Feeding her ego makes you just like every other guy ever. You must make yourself unlike the other guys. Cocky funny is your best bet then. At least of the two options.

There are other ways of dealing with conceited girls, but the number one thing to do is NOT feed her ego.

Cinnamon

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Treat her like anyone else, even ignore her and talk to one of her lesser attractive friends, if she tries to get attention or makes a comment shut her down with a light neg, like her being needy or something.

What are some other ways of dealing with conceited girls?

that is the most important thing DO NOT FEED HER EGO! because like he said thats what everyone else does. the way i like to think of it is say one of ur guy friends u met is cocky and always has to brag deal with it that way. i would neg her after she bragged about something and just give her the vibe that i dont care what shes bragging about and shes loosing my attention by bragging so much... like when i talk to a guy that brags alot i dont give a fuck wat he has to say if hes just talking about himself the whole damn time so u should treat a concited girl the same way but maybe alittle nicer haha

take her out of that state of mind.. being a much higher class guy than her and make her qualify herself to you.. like people say.. ignore her from time to time.. make her wonder why she's not getting attention from you unlike any other guy out there who practically throw themselves to her..