The Corpus of Contemporary American English (COCA) has 1650 incidences of kinda:
TOTAL SPOKEN FICTION MAGAZINE NEWSPAPER ACADEMIC
1650 172 1023 244 169 42
It is used overwhelmingly in fiction, and the few examples in newspapers and academic texts are almost exclusively in quotations of spoken English.
So, as the other answers have said, kinda is a pretty informal word, not used in formal texts except in quotations. I personally would only use the word in very informal situations. Its 1650 incidences in COCA are comparable to other adverbs, such as besides (1720), tight (1642), and regardless (1607). As to whether or not it is an “actual” word, I think this is pretty clear evidence that it is. As for its acceptability, it is listed in some dictionaries, including Random House and Merriam-Webster.