1. The quoted person actually said or wrote the words.
2. The quoted words are accurately reproduced.
This is easier said than done in the Internet age, as quotes run amok on-line.
Your safest bet to quote Kerouac and be sure he said or wrote the words (#1 above) is to get your quote directly from one of his published books. You then can rest assured that he wrote them (more or less -- publishers fuck up, too). It helps to cite the book title and copyright date and publisher and page number(s). Then quote away. Even if it doesn't meet #2 above, you can blame it on the source (as long as you reproduced accurately). This includes his published letters, which, again, if it doesn't meet #2, you can blame it on the source. Another option that is less safe is to quote a legitimate secondary source such as one of the many well-regarded biographies. This won't ensure meeting #2, but, once again, you can blame it on the source.
What you should not do is take a quote from Goodreads or any of the many other quotation sources on-line. They are often not cited at all, or correctly cited, and they are often not accurate. That is, they don't meet #1 or #2 above. Note the difficulty in capturing an accurate Kerouac quote that I posted about here.
One exception to this rule seems to be the Jack Kerouac Wikiquote. It seems to meet #1 and #2 and even includes a list of misattributed Kerouac quotes. If you find a mistake on there, fix it. Be part of the solution and not part of the problem.
Still, your best bet is to open a book like On The Road and carefully transcribe your Kerouac quote directly from the source.
And cite your work. For posterity. Please.