Ok, I have no I idea why that dimmable LED bulbs flicker when turing on an induction load, like for instance, a exhaust fan. For example, if you turn on the light in a laundry room, and then you turn on a exhaust fan (if wired in parallel with two switches each of them) you will notice a slight flicker when you put on an induction load. Now halogens and incandescent bulbs don't do that. Does this happen to you when using dimmable LED bulbs?

A bowling alley here has recently converted to LED strips. I was there on Sunday, and every time someone pushed the reset button to trigger the pinsetter cycle, the whole installation flickered slightly. I've never seen the equipment, but I believe there are two or three ~2HP motors that start for each cycle. The other motors that run continuously did not make the lights flicker. I don't believe they are dimmable LED, but I don't know.

It uses to be the triac hold-on and power regulation circuit being disturbed by the supply glitch.
The thing is, unlike the incandescents, with LED (and/or fluorescents) you can not control the power by phase cutting the supply directly. The main dimming functionality has to be done by the ballast, while the phase cut voltage is treated just as a command signal
The problem specially with LEDs is, they are very efficient, so draw just small current. Mainly at low settings, where the ballasts are programmed to mimic the dimming characteristics of an incandescent the currents become really low. So low, it may prevent the dimmers from operating correctly when not treated within the LED ballast.
So the ballasts contain a circuitry, which at first is damping all eventual oscillations of all the EME filters around the triac and as second, maintain certain minimum current through the triac ON phase.
On top of that users usually want minimum delay in the brightness response.
All this requires quite high gain response regulation scheme on the power control, so lead to pretty low regulation loop phase margins, which means it may start "hunting" for the target power before it settles once it becomes disturbed by something (e.g. the voltage dip).
And the short flicker is just the visible result of that "hunting".
Nondimmable versions do not have to "care" about the control range and triac operation, so are usually designed with way greater stability margins, so are way more robust against such disturbances (but with a tendency to kill the dimmers when connected behind them as the disadvantage).

CFLs do not suffer that much, mainly because the fluorescents loose their efficacy at low output settings, so their input power does not have to be reduced that much, but mainly because of the narrower dimming range, no one ever attempted to mimic the incandescent dimming characteristics. The LEDs are able of such range, so makers try to really match that very close. But that then has its consequences.