I use a porabrace smuggler case,its designed for carry on,you take off the eye piece and lens ofcourse.But no good for small jets as it wont fit into the overhead lockers.But for your trip it should be ok.
The UK will be the worst country for any hassles about getting gear onto the plane,that was always the case way before recent events!But you can now drive from UK to France on the car/train under the channel.Its a very easy trip.
I would very much try to avoid your gear being not allowed on at the last minute/at the gate,this can be worse than the hold! sometimes doesnt make the flight at all! and well may get chucked about more.
I believe flicker will only be from flories/sodium lights,ie ones on a cycle,but incandescent should be ok.
Yes a 1/00 shutter will deal with flories,but sodium lights can need scan,and are often an odd color.