Would flux do the job here? If so, what is it for, and how to you use it in relation to the iron and solder wire? Can you buy it anywhere other than an electronics store? (Don't have one of those locally.) Is the hardware store variety the same?
First off.
DO NOT USE ACID CORE SOLDER/FLUX!!!!!!!!
This is what you find in the plumbing dept. It will most likely work, for awhile, then the acid will corrode everything and make it all fail.Very bad stuff, big mess.
You may be able to find some rosin flux at Lowes in the electrical area if they have soldering irons/solder stuff. Radio shack should have rosin paste flux as well. You should be able to get some good flux wherever you got those leds. (I prefer the pen in the link because its really easy and less messy with no cleanup) Off the top of my head you may also be able to find it at Grainger, or other local electrical supply places.
You should be using rosin core solder, this does contain flux just not very much. Most of the time you do not need to add extra flux but when you need it you really need it. The flux would be applied to the soldering pads (B) where you attach the wires, if I was having problems I'd flux the tinned wires as well. The wires you are attaching to B should be stripped and tinned before attaching them.
Honestly, If the pad (B) and the wire are properly tinned, the iron is running the proper temp and you've got a good tip you shouldn't need extra flux.
Have you dressed the soldering iron tip with a file? This is a common problem, the tip will become "dead" over time and it needs to be cleaned up a bit to promote better heat transfer.
Are you using 60/40 Rosin core lead solder or some type of lead free stuff?