The photos are dreadful but it appears to be the standard rayon/cotton male sports vest with the pre-July 1938 small diamond. Later male vests had the larger swastika. There was a sports vest made specifically for the BDM and JM (see below). The pictures are from a 1936 publication.
Certainly as far as the regulations go it will be this item The RJF clothing regulations for the girls say "white sports top with HJ cloth diamond". The 1936 RZM manufacturing instructions show the item I mentioned in post #4 so we must conclude that the girls are indeed wearing it. Here are two examples of the BDM/JM sports vest: