What is the best tool for Amazon Kindle book publishing?
There are some very good, free EPUB editors like Calibre and Sigil (see bottom of page for files). Then you can upload that to Amazon. It has enough information to get converted to whatever format Amazon is using now. Better to have enough information in an EPUB than to fool with a Word DOC or DOCX which is frustrating for many people.
EPUB files support all kinds of meta information too, like multiple authors, multiple subjects (for library catalog classification).
I'm going to give the easiest answer -- though learning it can be hard.
Adobe Indesign lets you produce both pdfs and epub files (to convert into kindles).
If you want to do everything in one tool, then Indesign is your solution. (They charge a monthly fee for renting the software which is quite reasonable). Then you can convert the epub file to kindle .mobi file by using the Kindle Previewer.
Another solution is to pay a formatter or a publishing company to produce the book. Surprisingly, it is not particularly expensive (you can probably pay about $250-$500 for the job -- possibly less; I should know because that's the work I do). If you're not comfortable with technical stuff, paying for that might be easier.
Some more ebook options are discussed in the "Amazon Kindle Publishing Guidelines" (Version 2015.4) (For some reason, the URL is always changing; you may have to hunt a while on amazon.com to find it).
Finally there are several tools that I have not mentioned. For example, you can use MS Word to print a pretty awesome printed book. I have done this before using the MS templates specifically for books. (After googling "book MS Word template" I found a great template from one book designer for less than $50-- it looked great).
For producing epubs, you can use calibre or sigil or something similar.
The key thing is downloading the Kindle Previewer program from the Amazon site to convert from epub to .mobi
I'm making the production process sound a lot easier than it really is. For example, testing and quality control is quite complicated and time-consuming. But this is the basic information you need.