Direct propane heat will not work on FooKayaks2's vat since it is jacketed.
In my opinion , It will actually , assuming that the bottom is water jacketed as well , a flame would heat the water within the jacket which would in turn heat the milk in the vat , it would act as a kind of double boiler , and would be a very economical way to get set up.
As long as the jacket is vented and can't build pressure it would be safe.
It would however be a little hard to precisely control the temperature until you had it figured out , the water would continue to heat the milk for a time after the flame is shut off , but with practice , it could be done , even the double boilers are somewhat that way.
If there is no water jacket in the bottom , then no , it won't work.
Closed loop system would be better , but more costly.