A random thought,how well will braid designed for silver solder work with tin/lead solder,or vice versa
Copper wets very well with lead free, leaded, or silver bearing solder, it makes no difference. As long as the braid is made of clean pure copper, then any electronics solder will wet into it.
The "Amtech" flux that the OP is using may not be ideal. First, there is the possibility that it is fake. Second, even if genuine, the most popular Amtech NC-559 is a no-clean flux. A very important property of virtually all no-clean fluxes is that the fluxing action is very limited in duration. In other words, the soldering heat activates the flux so that it cleans the oxides from the surfaces, then -
this part is important - the chemicals are used up, which effectively de-activates the flux, and it no longer has any "fluxing" action. At that point, it is benign residue, which is exactly why it is considered "no-clean". At soldering iron temperatures (much higher than reflow), this happens within a few seconds
at most. When desoldering with braid, you will always exceed this heat/time, and deactivate the flux quite quickly. A no-clean flux core in solder wire is designed to fully activate then become benign within the 3 or so seconds it takes to hand solder a single joint.
Other types of flux are continuously active when hot, and inactive when cool. This is true of most Rosin flux (R - not activated, or most RMA - mildly activated, and some RA - activated). The residue is hard, crusty, and ugly, but can be safely left behind on most boards. There are exceptions to every rule: high moisture makes a difference, and some activators in some Rosin fluxes are not safe to leave. Always read the datasheet for your flux. If I rarely feel the need to add flux to braid/wick, I always choose a good quality RA or RMA flux, and never any type of rosin-free no-clean. If I could buy Kester 44 flux in a bottle, I would be in heaven. That stuff is just ridiculously amazingly good.
One tip for desoldering with braid: if the board is cold, forget it. I always reflow the joint first, with a little flux, making sure that the solder liquefies completely (including to the other side for through-hole). Then I quickly introduce the braid on top, and apply heat through the braid. Especially for through-hole components, if you only heat through the braid on a cold board, just the topmost solder will melt and wick into the braid, leaving behind most of the solder in the plated hole, protected from touching the wick by a nice air gap you created. The trick is getting all the solder to melt before the topmost bit disappears and disrupts the capillary action which pulls the solder out of the hole or from behind SMD IC legs.
I firmly disagree with jonpaul about "push the tip against the [braid]" and "Jiggle tip". If you apply force to a hot pad, it may delaminate from the board. This is especially true on single sided boards which do not have the benefit of a plated hole to hold the pad in place. Your iron tip should have a tiny amount of molten solder on it, which will conform to the shape of what it is applied to, and transfer heat effectively with only a light touch.