I have doubts you’ll be able to get enough heat into your handle and sleeve assembly to adequately flow the manganese bronze filler using MAP gas. You’ll need the entire portion of the assembly being brazed to be at 930°C which I’ve only ever done with Oxy-Acetylene.
The benefit of the silver is that it only requires around 650°C which is achievable with MAP, although you’ll still need to take care to ensure uniform heating.
That flux is for using when silver brazing all the listed things, I.e. it is a flux for silver rods. If you want to try brazing using bronze filler you need a flux specifically for brazing using bronze filler rods.
It should only require three rods to do the job. I think this is a fairly ambitious first brazing project; in order for it to work you’re going to need to have every factor lined up in your favour.
