I need to know what brush on matte varnish is the best. That doesn't leave any sign of glossiness or shininess what so ever. I would really want that absolute matte finish on my figures. Something like the following picture. Thank you.

It's not the brush that will leave a gloss or shine to the finish. The brush you use won't have any effect on the finish of the figure except for cleanliness of lines and smoothness of the finish. Not the shininess or matteness of the finish. That will be completely up to the type of finish you are using.

If you are using a Matte finish or sealant, then that is what you will end up with, a matte finish.

Brushes are mostly a personal preference, but you will probably be fine with a nice synthetic brush tip. Pay for a decent brush, DO NOT BUY CHEAP BRUSHES, they will "shed" bristles and leave very unsightly brush strokes.

My recommendation, go to your local hobby shop or Art supply store, buy a few different brushes, matte finishes (maybe even try a spray on version) and then head to the Dollar store for some cheap action figures.
And then ... its all PRACTICE PRACTICE PRACTICE.