Slate and tiled roofs let water in but then it stops at the underlapping slate and gradually goes down to the gutter.
If there is an underfloor, then that can catch any rogue drips that escape.
That looks a decent job, but at your vent i suspect that water can blow up over the top or side of the zinc and has nothing under it. Or some tiny gap where the slates are cut.
It would be necessary to take the ridge off to see how far the metal goes.. I think it should go all the way to the apex OR have another overlapping piece to intercept it. And wider too, hidden under the top slate.
Wind is the likely culprit. Gusts generally last just a few seconds, firing water upwards, but then releasing it. Hence a longer flashing might suffice.
mastic exists for flues but that should not be very hot there. It is nit very flexible so won't last long.Try a local stove shop.
There are special and foolproof rubber flashings for flues througb metal roofs but they are ugly and not appropriate to your lovely roof.