In general, the dielectric strength of a gas varies with the gap length, so for small gaps it's not strictly correct to say that air has a dielectric strength of 3 kV/mm or any other single value. [0] But at this scale, the gap is so small that the idea of "dielectric strength" isn't really meaningful anyway. There are so few atoms between the electrodes that electrons can flow with negligible resistance at any reasonable field strength.

[0] https://en.wikipedia.org/wiki/Paschen%27s_law