Is it illegal to distribute chapter 1 of books via an email newsletter in order to get subscribers to purchase said book through affiliate links?

Whether or not you may do so depends on complex issues of copyright law, including the application of the exception to copyright infringement called "fair use." If your purpose is to promote, rather than retard, sales of the hard copy, as Amazon does, then there would be a good argument that the use is "fair." Fair use determinations are always intensely fact-dependent.