"멋대로 깝칠깝칠" => willful and flippant [sassy, frivolous]. 깝칠깝칠 is not in wide use (dictionaries don't list it). Someone is using the verb 깝치다 like an adverb. Even 깝치다 (be frivolous and showy; impertinent) is listed as a nonstandard variation on 깝죽대다. 깝죽대다, or 깝죽거리다, as well as 까불다, 까불대다 and 까불거리다 are traditional words with the same meaning. So the phrase is describing a flippant attitude of someone.

I've never heard of the word before. Not used much in common life.

Let me make sure I've got it right some character in soap opera says '멋대로','깝칠깝칠'. and you want to know what this meant, Right? '멋대로' mean arbitrary, act willfully, and, maybe '까칠까칠' is right sentence, '까칠하다' mean picky and fastidious person If you don't understand my English or There are grammatical errors in my sentence Add some comment. thx