To be clear, it is illegal to use someone else's work in and as your own. You could take one sample - a literal .0001 second sample you didn't record and it would be illegal. If anyone else cared and they could prove it.
As a practical matter, not bloody likely. The copyright owner would have to "hear" your work and recognize their contribution and prove it in a court of law. Of course, there is the rub. James brown's estate likely has more money than you and a lawyer that is familiar w/ the process. If you made money off his work they would get all that you made and more. See The Verve V Rolling Stones.
If you are doing music professionally, it ain't worth it. As bit sez, find a library which like government work is close enough. Or do it yourself. Or if you have lots of money get one of the services that will replicate a Ringo snare hit by renting abbey road studios (the same room) and find the snare and head and kind of stick used on the session and do a "hit" for you. SOS had a lengthy article about that.
Practically, if you just want to muck around and take a james brown "ugh" and muck it up and layer w/ a hippo fart and lion roar and use it on a self-produced CD that you hand out to family on Christmas you aren't likely to suffer any repercussions. Nobody will hear it, and if they do won't know where you got it. And even if they did, they would demand you destroy any remaining copies and give them the "master tape".
Two real examples. Todd Haynes, the film maker, did an early film using a Barbie doll in Superstar, the Karen Carpenter Story. You won't find a copy, (tho it is on youtube) not because the Carpenter family objected (she was a public figure, after all), but Mattel objected to the use of copyrighted Barbie. It was a crude, underground film that caught on by an experimental artist right out of college. Of course, the PR was great and Todd went on to do Hollywood (he's a talented guy, which never hurts, even in Hollywood). The other was at the same time in NYC (80's). I did sound for him in the after hours clubs he promoted. One of his other ventures was selling baseball caps when wearing them backwards became a "thing" (before then the only person to wear them so was Goober from Andy Griffith). He had some with "Coco and/or "Chanel" made and sold them to downtown shops. Of course, NYC was a fashion central and the hats got play in the fashion/lifestyle rags as well as the streets and cool people parties. He sold about a 1000. All that happened was he got a cease and desist letter from Coco's lawyers.
Draw your own conclusions.
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