Had a thought today that what I really need is a phone screen cover that is only in use when the phone is in the pocket of these particular trousers. Ding!  Rather than have the cover on the phone as in a flip case why not put the cover in the pocket?  Had a look online for such a thing but no joy so started casting around the house for something I could use  And Lo!, sitting on the desk by my old desktop PC which has not been turned on in years, under a mouse which has not been moved in years was a rubberised mouse mat.  The perfect combination of stiffness and flexibility with a soft surface  and easily cut to the shape of the pocket with a pair of scissors.  Sometimes the simplest solutions are the best but I will report back after giving it a road test.
Edit:  Found that just folding the mouse mat in two allows it to slip easily into the pocket with hopefully sufficient coverage.  Will try scoring the crease line with a sharp knife to get a sharper fold ...