Red slime is actually a bacterium, which is properly reffered to as Cyano bacteria
Cyano Bacteria is commonly caused by a high phosphate level, high nutrient level, low oxygen level or high biological level. Elevated phosphates can easily trigger unwanted outbreaks of this bacteria. High nutrient levels in the water also play a role in the Bacteria growth. A low Flow rate also helps the bacteria spread very easily, without being blasted off the rocks and/or substrate. Cyanobacteria also has a very hard time staying alive in oxygen rich water with good flow. Cyano must reach anaerobic levels to live.
The best method of removel is to always use Reverse Osmosis (RO, or possibly RO/DI) water and possibly a phosphate sponge. This will eliminate any harmfull chemicals going into your water column and causing a problem. A phosphate test kit would really come in handy to see if your tank has phosphate.
More information on your tank setup should really help, esspecially your flow rate and tank demensions. Also, when did you start up the tank, when did the cyano bacteria start? Did you do any changes in anything prior to the outbreak?
Graham