Hmm... I just gave up trying to use windows to cross-compile for the kindle at a very early stage so I sadly can't help there. However knc1 provides the entire set of x-compile toolchains HERE
http://drpbox.knetconnect.com/KeK/ - This AFAIK includes a mingw32 that works on a
correctly configured windows box - The toolchain for 2012 is
http://drpbox.knetconnect.com/KeK/ar...ingw32.tar.bz2 for example...
I also have not used DSL... BUT...
http://damnsmalllinux.org/packages.html indicates that it has apt. so you have a couple of choices. Either apt-get something down from a debian repository into DSL or use the windows option.
Both options will probably require a smidgen of massage to get going initially. HTH.