rar isn't available for armel/armhf Linux. It's proprietary archiver with closed source and developer didn't compiled it for discussed [KT] platform.
However, unrar utility is provided with sources, so it could be found in compiled form for armel/armhf Linux. As
knc1 said, you can extract it from appropriate Debian package.
Debian archive could be searched for needed package at
http://http://www.debian.org/distrib/packages. Or by shortcut: http://packages.debian.org/<package name>.
So, go to
http://packages.debian.org/unrar. As you will see, there is unrar package and it's available for armel (and, starting from Wheezy, for armhf) architecture. Look for most recent version, then press on nearby link, which is looking like:
sid (unstable) (choice of
sid is just example) and you'll land on package page. At the end of page, there is list of links to this package compiled for various architectures. Click on
armhf armel link (thanks to
baf for
pointing to advantages of armhf over
armel; but stock Kindle libraries aren't compiled with
armhf ABI, so for dynamically linked binaries one should use
armel-specific variant), and you'll land on page with direct links to package on archive mirrors. Click on any of them and you'll download the package.
.deb package is an
ar archive containing compressed
tar archives (
more info). So if you're ok with using of
ar and
tar utilities, you can unpack downloaded .deb, then unpack
data.tar.gz, and you'll find
unrar-nonfree binary at the path
usr/bin. Otherwise, try to look for online services which could unpack
ar/
tar (or, maybe,
deb).