Can I give away a book on my website that is for sale on Kindle?
You can sell a book through KDP (Kindle Direct Publishing) and sell it other places such as your website or Barnes & Noble or Kobo, etc. The only limitation about selling it in other places or giving it away is if you join the lending library by enrolling in KDP Select, in which case digital versions have to be exclusive to Amazon for the 90 day enrollment period.
As long as you don't have it in the Select program, though, you can feel free to give it away or sell it elsewhere. Amazon may notice a different price (including free) and then price match, which can effect your commissions (or get rid of them altogether) but if it isn't a concern of yours then that won't matter. (And if it is, then don't put the separate pricing in a public place where Amazon is likely to find it!)