I've used chemiclean in the past and it works.. but the slime just comes back.. I think you are just temporarily getting rid of the algae but not getting to the bottom of the thing that is causing the slime.
Now I haven't tried this myself but I've ben told and have read that the zeo coral snow works really well for red slime. You don't have to be running zeo to use it either.
http://www.jlaquatics.com/phpstore/s..._ID=zv-csnow02