You could probably get a debate going among grammarians as to whether or not this usage is grammatical, so I would not worry too much about that.
However, this is accepted English usage in informal situations. Its use is not advised in formal business or academic writing.
Is 'Not' a complete sentence. I won't get into this argument here, but you may also get a debate going on this point as well. There are many other single words that are used as 'sentences', eg, Go, Yes, No, Stop, Person's name (e.g. Peter), Whoa, Never, many swearwords, etc.
As for 'Kind of'. This would still not be considered to be a sentence using the normal standards of grammar. However, any person who has raised children will have heard 'Kind of' as an answer to hundreds of questions directed to them, e.g.:
Did you clean your room?
Have you done your homework?
Did you hit your bother first?
And it is not just children who use this non-answering answer.
I think that the use of 'Kind of' is well attested in informal spoken English, and is at least as acceptable as 'Not', so I would hazard a guess that like 'Not' it is acceptable, but not grammatical.