http://linux.palemoon.org/help/installation/
It should be noted that it is not necessary to install Pale Moon to use it.
It is distributed as an bzipped tarball which can be extracted anywhere and run by executing the "palemoon" file inside it.
http://linux.palemoon.org/help/faq/#portable
Is there a portable version of Pale Moon for Linux?
A Windows "PortableApps" style application is not possible due to filesystem permission restrictions on Linux.
However, if you mean "portable" as in no installation needed, Pale Moon for Linux is already in such a state! Just grab the archive you want,
extract it anywhere you like and run the "palemoon" file.
For your reading pleasure, more install-ish stuffs here: http://linux.palemoon.org/help/installation/
FWIW, here, I see a post dated Nov 12, 2015 announcing "Slackbuilds.org now has a Pale Moon slackbuild"
http://forum.palemoon.org/viewforum.php?f=37
also FWIW, in case you care about privacy/cleanup
palemoon shits it files "all over the place" and, last I checked, bleachbit doesn't know locations for the various palemoon cleanup targets
(macromedia/flash .sol cookies, mozilla cache, sqlite files for vacuuming, etc.)