Brady,
German FlaK weapons (even the weapons on SPAA) generally only carried AP in small 'self defense' quantities.
Usually it was between 10-20% of the total ammunition loadout.
Everyone:
Be careful when looking at ammunition performance tables, especially for the 3.7cm German weapons. There was a big muzzle loaded HEAT round made for the 3.7cm PaK 36 (effective range of ~100 meters, ROF very slow - single shot muzzle loaded, etc.) to give it a chance vs. the T-34 and KV-1 (and if it hit it would really do some damage - 3.7cm was the size of the rod that went into the muzzle of the AT gun, the warhead was a very big HEAT warhead). So if you are perusing a table of German 3.7cm ammunition and come across a HEAT round that has a huge penetration value...that's what you are seeing.
APCR (tungsten core in this case) ammunition for the 3.7cm was used almost exclusively for PaK and big AT guns on aircraft. I've never seen accounts of it carried or used by FlaK weapons (and this includes actual AARs from German units) and 3.7cm KwK weapons might have carried 1 or 2 rounds total per vehicle.
Mike/wulfie