Can someone tell me how long does the voltage kick from the choke in a preheat ballast last for? Is it milliseconds or longer?
It depends, how high the voltage is allowed to go and on the exact current at the instant the starter opens.
To find it out exactly, you need to go through some math (and physics).
The ballast is an inductor, where the induced voltage is given by the faradays law of induction, which could be flipped to describe an inductor as a component would look like:
V = L * dI/dt.
When the inductor is connected to a voltage source (so the voltage is forced externally), the current will evolve in such way, the induced voltage equals the connected voltage source (well, at this point I neglect the wire resistance). So when you want to know the current, just integrate the equation, you will end up in an equation for the current:
I = 1/L * int(V * dt) + I(0)
The I(0) is the coil current at the "t=zero" moment, mathematically it is the integration constant. Practically it depend on the history before the evaluated event.
From that you may see, once the connected voltage becomes a nonzero constant (= DC voltage source), the current will rise over time to infinity, hence the "short circuit to DC" behavior).
Now in the case of the ignition event in a preheat ballast, at the moment the starter opens (let's assume that happens at t=0), the I(0) would be the instant current in the ballast at that moment (it could be anything between zero and peak current during the preheat, depend on when exactly the starter opens within the current AC cycle). Just when the starter opens, the current will find other way than the closed contacts (the immediate collapse can not occure, as it would mean an infinite voltage), normally it is either the lamp (some 100's V) or discharge in the starter (nearly a kV at this current). The pulse ends at the moment, when the current reaches zero. By evaluating the integral above, you end up:
Tpulse = I(0) * L / Vpk
Tpulse is the voltage pulse duration, Vpk is the voltage of that pulse; Assume constant voltage over the complete pulse.
Now what is the exact L and maximum I(0)?
Now as the current was formed by the mains (so an AC voltage source), it's peak value would correspond to:
I(0) = 1.414 * Vmainsrms / (2*Pi*Freq) / L
When replacing the I(0) for the equation for the current:
Tpulse = 1.414 * Vmainsrms / (2*Pi*Freq) / L * L / Vpk = 1.414 * Vmainsrms / Vpk / (2 * Pi * Freq)
And you see the ballast inductance had disappeared, so we don't care about it's value (ballast rating,...) nor changes with current (saturation,...), just the voltages and mains frequency.
So with 230V/50Hz mains and about 500V pulse (the cold electrode discharge across a not yet warmed fluorescent tube), you end up with about 2ms pulse.
With 120V/60Hz and 300V across the lamp (assume shorter lamp, used in 120V circuits), it would be about 1.5ms.
But when the lamp is missing and the pulse is limited by the starter (assume 1kV), you end up about 300us (for the 120V case).