I am not in slackware (fedora kde) but I have the same issue in both konqueror and firefox. I checked Adobe and I have the newest flash version available. I started looking for a fix and found this post:
"I ran across a discussion related to this stating that Google wants to use the H.264 (patent issues) standard for youtube to move users from firefox (open source) to chrome (closed source) since there's an issue with firefox supporting the H.264 standard. The reasoning this being that since google and youtube are the #2 and #3 websites, users will switch to whatever browser gives them the best access the sites they want. I am not sure why there couldn't be a plugin to handle H.264 the same way that flash is handled, although with flash there are libre alternatives, where as with H.264 I don't think so. There are other people that must know more about this and perhaps another thread is the best place to discuss it... just my thoughts. In any case, another reason to support free (libre) software and standards."
The poster didn't include a link to the discussion so I couldn't verify any of that. I did happen to have firefox, konqueror, and chrome all installed. Any video I try from youtube gets the rude "go upgrade" message in firefox and konqueror but plays just fine in chrome. Disabling adblock/noscript/cookie rejection/pop up blockers for firefox and konqueror did not change anything.
A possible fix posted on that same page is:
"You should be able to watch videos on youtube, as well as links to youtube videos on other sites without flash at all. Just install greasemonkey, then download and install the scripts from http://userscripts.org/scripts/show/50771
. They are all free software; greasemonkey is under the X11 license, the first script is under the GPL, and the second script is in the public domain."
I have not tried that yet so I do not know if or how well it works.