tkt is SMS lingo for t’inquiète, shortened form of ne t’inquiète pas. It has the same usage as don’t worry or that is all right in English.

— Désolé pour hier soir
— T’inquiète

— Sorry for last night
— Don’t worry, that’s all right

And, recently, I believe, it has started to be used to emphasize an affirmation

— Oh, t’as la classe, ce soir
— T’inquiète, bien sûr que j’ai la classe

— Wow, you’re classy, tonight
— You bet your ass I am¹

but this usage still sounds very banlieusard.

¹ Fell free to correct my attempts at American English slang.

This is precisely the same thing English people tend to use some time that is np for No Problem.