You can do this, but it would require chrooting into an image of an actual distro.
From the blog you referenced:
Quote:
[...] inside a chrooted Debian ARM installation I put on the device. Having Debian on the device isn't really necessary for hacking the Kindle but it does make it easier to install ARM binaries of just about any of the 25,000 packages in Debian. Yep, apt-get works on my Kindle!
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Further reference:
Debian_Installation_on_Kindle_Touch
IOW, no the Kindle does not have apt-get preinstalled, since it isn't actually a debian OS...