Looks like Broadcom might finally be coming to the party - have a look
this.
Previously would probably have needed fwcutter. Note I don't know if this works with Slack - I specifically bought the Intel chip, but that was over a year ago.
Search here on LQ for "slack broadcom" or bcm4322 - should get plenty of hits should you need some help.
Edit: looking at that README, note that everything after the untar will need to be done as root. You might want to start a new thread in the slackware forum once you start, as you probably will need some (slack specific) help.