Personally, I find that vacuum desoldering pumps can be a little flakey, and their recoil isn't always welcome around more delicate circuits. For braid, I find it's best to put the braid between the iron and the target, and let the copper conduct the heat directly into the solder that you're trying to melt. The desoldering that I've done hasn't required any flux, tbh. When you're putting a new component on, on the other hand...
__________________ i7 2600K | ASUS Maximus IV GENE-Z | GTX Titan | Corsair DDR3-2133 |