Oldsmobile, and a very few Buicks had a Hydramatic in 1938 and 39. Those transmissions had a manual clutch, however. It was necessary to disengage the clutch for stopping, but once in motion, the shifting was automatic. The 1940 models were the first to have a fluid coupling (not a torque converter). The fluid coupling locks up at almost 100% RPM with very little slip, whioch is one reason the shifting feels rough. Torque converters have 10% slippage built in by their design.
Throttle pressure adjustment is very critical. It's adjusted by changing the length of a rod or cable from the carb to the transmission. Too much, and the shift is harsh. To little, and there's a lot of slip (called "flare") on a shift, resulting in rapid wear on the multi-disc clutches inside the transmission. A little rough on the shift is better for long life of the trans.
A place called FATSCO Transmission Parts carries a good supply of rebuild parts, some of them original-equipment. They've got a website, so do a Google search for them.
Jerry