In a dowel, you can't tell. Once turned round there's no way to know how it was milled. In a square, you can have a fair idea if you can see the entire lot. With squares, if the grain runs diagonal on much of, at least half of the lot, then it's been flat sawn. Quarter sawn wood will leave ALL the squares with the grain running parallel to edge. So if you see a pallet of shaft squares & none of the grain runs diagonal across the end grain, then it's a very good chance the wood was quarter sawn.
In quartered lumber, the grain will all run down the face of the board, none on the edge of the board. In flat sawn, most of the boards will have grain running along the edge of the board, some at an angle, and a few out of the center that will be quarter sawn with the grain running down the face. Flat sawn lumber is irregular from board to board where quarter sawn is pretty consistent in grain orientation to the boards.
The major difference with quarter sawn wood and flat sawn wood is stability. With flat sawn, it has to be strapped down in the kiln to keep it from warping, cupping, curling, bowing, twisting, cracking, etc. Once dry it's flat lumber but full of internal stress. This is why it binds & twists when being cut into squares, and moves during the shaft making process. It takes a long time to get them stabilized & even then it's a high waste deal.
Quarter sawn wood is relieved of stress by the cut, before it's dried. It can be stacked & stickered in the kiln with no binding & once dry it's still flat & crack free & stable. I just cut four logs last winter, quarter milled & dried them to 4%, then cut shaft squares & dowelled them. Cutting the boards to squares, then dowelling the squares took a day. That same day I grabbed two random dowels & in one thick, full cut, took them to a 13mm tapered shaft, finish size. That was 2 weeks ago & both shafts are still very much straight. Neither has been hung up. One was laid flat on the concrete floor & the other suspended horizonally over a lathe, resting on the ends with no support undewr the middle 20". I have no doubt in the world that quarter sawn wood makes the most stable & stress free shafts. I have proven that to myself. The entire experiment was to process shafts from trees & knowing everything every step of the way with no questions or doubts about how the wood had been processed because I did it myself. My conclusion was/is that i'll likely never buy another maple board or shaft blank in my life because I haven't found any that left me without doubt. Doing it this way gives me piece of mind.