Not sure this is headgear insignia, might be for the breast or lapel …
My best guess is that VeKD stands for "Verband Evangelischer Kirchenchöre Deutschlands" (union or league of protestant church choirs). The official abbreviation of the organisation was VeK (and then the D stands for Deutschland, Germany).
Was founded in 1883 and active during the Third Reich era. Still exists today, but under a different name.
In 1933, the league also became a part of the "Reichsverband für evangelische Kirchenmusik" (national league for protestant church music), so the VeK might stand for "Verband evangelischer Kirchenmusik" (although that may be a bit far-fetched).
It's tough finding these obscure leagues and associations as they had one for pretty much everything (canoeing, amateur photography, you name it!). Best of luck, hope I could get the ball rolling!