Which one of these three files would be best
to install ? I've got a version of Slackware
that says Linux 3.10.17 on the command line.

From the ffmpeg web site: ffmpeg-3.3.2.tar.bz2
From sourceforge ffmeg.0.4.6.tar.gz
From sourceforge ffmeg.0.4.8.tar.gz

I've noticed that installpkg does not list .bz2
files. Does that mean Slackware will not install
the file I got from the ffmpeg web site ?
Any information would be welcome.
Thank you for your time.

installpkg will only install Slackware packages which are *.tgz or *.txz files. The three files you list are probably source files instead of packages.
I'd recommend you either compile/install a package from slackbuild.org or install a pre-compiled package from AlienBOB's repository. You'll need to know your version of Slackware. To figure that out look at the file /etc/slackware-version.

-current comes with 3.3.2 these days.

If you're not running -current, consider this package:

http://bear.alienbase.nl/mirrors/peo...builds/ffmpeg/

Or building your own using this script:

https://www.slackbuilds.org/reposito...imedia/ffmpeg/

The files you mention contain the ffmpeg sourcecode. A Slackware package contains compiled code, aka binaries.
Your 3.10.17 kernel version indicates that you are running Slackware 14.1 but you do not mention whether this is a 32bit or a 64bit Slackware.
If you want a ffmpeg package for 64bit Slackware 14.1, get this one: http://bear.alienbase.nl/mirrors/peo..._64-1alien.txz
The 32bit package is here: http://bear.alienbase.nl/mirrors/peo...486-1alien.txz

You install a new package on Slackware using the 'installpkg' program. Provide the full path to the package you just downloaded as the single parameter to the installpkg command.

If you want a newer version of ffmpeg (3.3.2 is the newest) then you need to download the SlackBuild script and related files, and compile a package yourself. The location to download the script was provided by dugan in his reply.

Something unrelated to your initial question...

Since you mention you're running 3.10.17, that tells me your running an unpatched version of 14.1. There have been many patches put out to fix security vulnerabilities, so I'd recommend looking into keeping your Slackware up-to-date.

NOTE: That does not mean you need to upgrade to 14.2 if you don't want to...

This is for 14.1:
http://slackbuilds.org/repository/14...imedia/ffmpeg/