Kindle and BookTok actually play together in a weirdly specific way. You can absolutely get some of those viral BookTok titles for free through Kindle Unlimited or Prime Reading if you have those subscriptions—they download right to your device, zero ads, totally offline. But the real 'free' stuff, the permanently free ebooks outside subscriptions? Those are usually the first-in-a-series hooks or older public domain works. They're downloaded via the 'Buy now with 1-Click' but at a $0.00 price, and yeah, they're yours, ad-free.
The catch I've noticed is that the super trending, brand-new BookTok hits? They're rarely in that permanent free pile. You might get a sample chapter pushed as a free download, which is also offline, but the full thing usually needs a purchase or a KU borrow. Sometimes the algorithm on the Kindle store itself is better for finding those temporary free promotions than scrolling TikTok. I grabbed 'The Love Hypothesis' when it was a Kindle Daily Deal for free ages ago, and it's still sitting ad-free on my old Paperwhite.