Slackware drivers work with Redhat and FreeBSD
 

Will Slackware drivers run on other Linux distributions? Will they run on the various Unix distributions?

Can you specify exactly on what you mena by slackware drivers? Is it simply a package then you might be able to install it though it's better searching a package that's for your distro. If you mean kernel driver it could be too though it would be easiest to get working when made against the new kernel (unless you copy the complete kernel from slackware, but I guess that won't work with freebsd).

I was looking for linux drivers on a hardware manufactureres website. They had different drivers for Slackware, Redhat, and I think SuSE.

If there's one package with .tar.gz you can use it for all. Otherwise there's a package called alien which can create a package for another distribution.