Yeah they make AN fittings smaller than 3/16 I believe. We had some 3/16 tubing on the plane for priming the engine.

AN fittings are 37 degrees when flared correctly, while brake lines are flared at 45 degrees. Most flare tools are 45 degrees so to be done right, you should invest in a 37 degree tool. Although you should be fine with a 45 degree tool as the pressure is so low, and it wouldn't matter a whole lot if you did have a leak