Back in the old days commercial studios used to have a bank of cassette players to record quick tapes for the clients. You'd often see a bunch of Nakamichi cassette recorders in a side room. Kind of the same idea as burning a CD of a session or a temp mix now.
So the most efficient way to do what you are describing would be to buy a number of cassette machines so that you could record several cassette's in a single pass. To do them one at a time would be very time consuming and depending on how many you need to copy, not practical.
The signal flow would be from the output of your CD player (or DAW) to a signal distribution box where the signal would be multed, to the inputs of the cassette machines.
It's a bit of an annoying process because you can't do it untended, you have to watch the machines because of the pause and flip thing.
Incidentally, you don't "burn" cassette's, you record them.
