What was the first time the technology to produce a radial installation with pressure-cowls -w- baffling, and cowl flaps came into being? What was the first aircraft to have such a set-up?
I have no idea.
What made the baffling and induction system so intricate? Did the technology exist before this to produce a three to four row radial?
Technology was a progressive thing. There's really not a lot of technological increase in the engines introduced during the war years, other than they were a steady development to bigger and better using the same general technology. The biggest advent in power production wasn't the 4360 having more cylinders. The most technologically advanced radial was the R3350, with it's three power recovery turbines.
The 4360, in my opinion, is one of the best sounding of any radial ever built. Listening to the C97 idle was like listening to a symphony.
Baffling is intricate in any installation, in that minor changes in the baffles can result in hot spots, insufficient cooling and can shorten engine life or even lead to cylinder cracking. Baffling on any piston engine, not just radial engines, is crucial, particular to the individual installation. That is to say, an engine in one installation isn't necessarily baffled like the same engine in a different aircraft. In twin radial aircraft, the baffle arrangement isn't that complex, but it was especially critical in the 4360, for cooling to the aft cylinders.