disclaimer!!! My painting style and skill level is decidedly "table-top" and quick. I hate playing with something that's not painted and I cannot stand having miniatures laying around unpainted for long periods of time. The advice and pics you get from most other people here are probably going to yield better if slower results.
1. What colors should I use? Obviously I want to make them varied as they are supposed to be a "mob."
Everything!

Use lots of browns mixed with occasional color. I painted mine almost entirely with just bestial brown, kemri brown, and vermin brown. Throw in the odd red, green, or blue piece of clothing. Throw your desired skin tone on and voila! Wash everything with Devlan Mud to give it that dirty appearance, only thing left is to do the metal bits. Works really well and its quick!
2. General painting advice on the Flaggelant models?
Balancing making them look like a mob and just making them look.... blah is the tough part. Try to find 2 or 3 colors that will unify the unit in some way. Using a wash can help since it will shade the colors to about the same level, reducing the contrast of colors you usually wouldn't put together.
3. If you painted Flaggelants before did you use any techniques that worked really well?
The trick to washing so many different colors like beige, greens, purple, skin, and dark browns with devlan mud is to control the wash and water it down to different levels as you apply it. On the beige areas you will want to be careful about where the wash runs and you will probably water it down quite a bit. I think most people think of using a wash as literally giving your miniature a bath in the stuff, which is not usually ideal. Applying a wash well takes some patience and technique, like everything else about painting tiny little people!