Filtering the beer removes the yeast from it, so if you filter and then bottle with priming sugar you will just get flat beer. The only way to filter and bottle beer is to filter your beer into a keg, then artificially carbonate it, and then bottle it from the keg using a counter-pressure bottle filler or beer gun.
Carbonating with Kegs Forced Carbonation – By far the most common carbonation method for kegs is forced carbonation. In this method you simply refrigerate the keg and then apply CO2 pressure to it. Over a few days, the CO2 will permeate the beer and carbonate it fully.