Air gap for a coil calculation
We could just plug numbers into the formula, but it's more instructive to do it from first principles. Then if you forget the exact form of the formula, you can re-derive it.
You've already suggested some numbers for turns and pole area, so let's do it for a specific airgap as well, say 1 mm. Inductance is inversely proportional to it (assuming perfect magnetic material), so it's easy to scale afterwards.
Inductance is flux linkage per amp.
1 amp in 30 turns is 30 Ampere.Turns. This produces an H field across a 1 mm airgap of 30 kA/m.
This produces a B field in the airgap of μ0H = 4π*10-7 * 30k = 37.7 mT
This produces a flux of B*pole_area = 37.7m * 100μ = 3.77 μW
This produces a total flux linkage of flux*turns = 113 μW
So the inductance with a 1 mm airgap would be 113 μH.
On the face of it, all we have to do is scale down the airgap from 1 mm to 113 μm to get 1 mH. However, with an airgap this small, I doubt that we could approximate the magnetic core as ideal, and so the actual gap would need to be reduced further to allow for the finite reluctance of the core.