Have look at the brand new Forum section "K-Meleon in Linux".
You can use the unofficial variation K-Meleon-F353, from here :
or one of my adapted variations from the page for
unofficial K-Meleons, from here :
Read the notes concerning the different variations.
After installing wine, add the necessary Windows dlls
to the main folder of the unpacked K-Meleon zip-file.
You will need the files msvcp71.dll and msvcr71.dll
in your K-Meleon main folder.
The variations based on Firefox 3 and on Seamonkey 2 will
also need mfc71u.dll in the K-Meleon main folder to work.
If you don't have these dll's, look for them in the Internet.
Install K-Meleon unzipping it to a folder where you
have all user rights, for example /home/ubuntu or /opt.
If you want or need your profile in the ".wine" folder
because of rights problems, rename the file "profile.ini"
inside the K-Meleon main folder to "profile.ini-renamed"
before the first browser start.
I hope that you will succeed. If you have others questions,
I will try to help as good as I can.