The flux helps to clean the surface and allow proper flow & wetting. It may not require extra flux but I like flux and it cleans easy enough with alcohol and a cut down acid brush.The rosin core solder will tin wire pretty well, but may not be enough for the cup. If you can get the flux, do it. I'd dip the tinned wire in it, insert into the cup, then add heat. I haven't tried using a torch, only an iron or the current tweezers. The current tweezers are great for pin cups as solder will follow/ flow towards the source of heat. If you use an iron, it is likely to get a little solder on the outside of the cup. The tweezers just conduct current and the pin itself acts like a heating element. You can get a small tube at Radio Shack or any electronic component shop.
There was a surplus electronics shop in Denver, but I haven't been there in 7 years... no idea the name of the place and I did drive to get there, but it was just south, south east of down town. Cool old building with all kinds of electronic geek shit!