Last year I tried getting my library onto my phone and tablet after reading primarily on my laptop for ages, and it was a bit of a headache at first. Wuxiaworld's integration with Amazon's ecosystem isn't as seamless as, say, Kindle Unlimited titles you buy directly from the store. You can read them on multiple devices, but it requires a couple of specific steps. First, you need to download the official Kindle app on each gadget and log in with the same Amazon account. Then, you have to manually deliver the book from your Kindle library's 'Archived Items' or 'Cloud' section to the device you're using.
I found that the sync itself—the famous 'furthest page read' feature—does work, but it's slow and sometimes buggy. I'd finish a chapter on my iPad, pick up my phone an hour later, and it would take a few refreshes or even reopening the app to get it to jump to the right spot. It's functional, not flawless. The real annoyance is that if you sideload any non-DRM files, those obviously won't sync at all, so your place in a fan-translated EPUB is stuck on one device.
For stuff officially licensed through Wuxiaworld's partnership, it's manageable. Just don't expect the instant, perfect syncing you might get with a big publisher's ebook. I mostly stick to one main device for a given series now to avoid the hiccups.