Brian, I guess from the EBay link you are in Australia? The small blow lamp therein is way too small for the work you are doing, they are very useful for small work and I use mine (similar type) a lot for many different jobs.
Jason's is spot on regarding the heat you applied, way to hot, a good indicator when soldering copper or brass is that the flame goes green when the soldering temperature is reached and at this point little or no extra heat is required so just "play" the flame on and off the work to hold the temperature whilst you apply the solder.
For flux I would use a resin, Fluxite or similar or you can use the self cleaning flux sold at plumbers merchants, usually a white paste. Although it says self cleaning do not assume that it's a get out of jail free solution, you still need to clean your work before hand. With soldering cleanliness is next to godliness ! The lead free solder which is more or less pure tin is also very good but it flows freer than tinmans solder.
Clean and flux all your joints then apply heat, watch for the colour change then apply solder with a little extra flux if you wish. Works for me every time !
Regards John