Swarm TileGen Distributing your map
When doing "File -> Export VMF", TileGen will save your map file as: swarm/maps/output.vmf. You can copy this to your mapsrc folder and then open it in Hammer to work on it.
You can do quick multiplayer testing of your TileGen map by launching your map from TileGen and having other players connect directly to your game. They will each download the .layout file and compile the map on their machine. This should not be a final solution for distributing your TileGen map, as the map has no overview text file and isn't part of a campaign so will not appear in any of the game's menus.
Distributing as a addon
See Swarm Campaign Add-on Tutorial to turn your map into a complete, easily distributable addon.