It could be that the solder you have is not flux-cored, if it came in a it with separate flux.I soldered wires with a Weller soldering gun and paste flux it comes with and solder soaked into wires.
You may be better off buying some cored solder intended for electrical / electronics use.
Also note that the tips of the Weller "gun" style thing can get far too hot for small electronics use and are often just too big to do fine work; you need to be extremely careful with those.
Iron tips for electronics use are normally quite small, eg. the commonest size we use is 2.3mm across, like this: