Bit of a puzzle, here. I simulated the constant current coil driver circuit from the valve data sheet in two different configurations, using LTSpice.
The first is the manufacturer's design, and it performs better than I expected. The second simulation is with the coil in the collector circuit, with a flyback diode, and it oscillates at 29 kHz. I don't understand the oscillation, and wonder if it could be an artifact of the way LTSpice works (it is specialized for switching power supplies).
I could only guess at the inductance of the valve coil, and 1 mH may be too high (series resistance is 12 Ohms, as per the data sheet).
Screenshots of the schematic and coil current trace below. It looks like the manufacturer's design is OK.
Don't know anything about SPICE, etc. The inductance of the coil, snubbed by the diode, will in fact oscillate with an extremely damped oscillation. The current induced by the collapsing magnetic field when the driving voltage disappears will be dissipated by the coil resistance, at the same time will induce a reverse current in the coil. All should go to zero in 1ms, or less.
Is this what you are seeing?