This works on my X-T3, haven't tried it on other X cameras:
1) Zoom lens set to auto aperture "A"
2) Set shutter manually
3) Set an ISO value manually so the aperture result is above 5.6 or more (aperture number is white, not orange).
4) Then hit AE-L (auto exposure lock) button next to viewfinder. Do a zoom!
On my Fuji 10-24 f4 on X-T3, this eliminates the exposure stepping flicker during zooms,
but you will see a slight darkening at the telephoto end.
This is the natural behavior of most zoom lenses. The lens is not really constant aperture.
Normally the camera compensates for the brightness change from wide to telephoto by opening the aperture through a series of 1/3rd stop steps to keep the exposure constant. (When zooming the other way it is closing the aperture. Note that in the Youtube video above the first zoom out shows a darkening for each flicker.)
Put your ear to the lens and you might hear a faint clicking with the camera on and turning the zoom.
The lens in your case is probably f2.8 at the telephoto end but may actually be a stop faster at the wide end.
The Fuji 18-55 does three exposure steps (one stop) over its zoom range (unless wide open),
but at least here the lens is labeled f2.8-4 which is more accurate.
In other cameras the apertures may be changing more gradually without stepping, which would make the aperture changes invisible.
If need be, I take out the natural darkening of the "locked" zoom shots in my NLE software with keyframed exposure adjustments to gradually bring the brightness back up across a zoom.
You can also do this with vintage manual SLR zoom lenses.
