Well, by means of an update, I've been doing some more testing. The flickering can last for a looooong time after a cold start with the meter, but gradually gets shorter as the meter's off time reduces.
BUT, I found that I can stop the flickering immediately by pressing the Range button to force it out of its Auto AC/DC startup mode (when it has 'TEST' showing in the display). So, in my case, with a 1.2V battery, I get 1.234 digits by the meter's default display on power up. and it is the lower two digits that flicker. RANGE takes it out of Autorange and into manual, and for this battery, the manual range is 1.234, e.g. no different from what it was before pressing the RANGE button, except that the flicker stops, and the word TEST (and AUTOrange) disappear from the display.
This seems to point to me to be a software flicker rather than a hardware noise issue, the meter's startup filtering might be doing something to small signals that is not quite right, but force it to change range with more digits and the problem stops.
An interesting problem, and an example of how software manipulation of values can sometimes give you unexpected results.
And another reminder to me, from my earlier T&M days (40+ years ago, cough) that I shouldn't be surprised when values in the lower part of a range could have significant errors in them (e.g. 0.03% +20digits, is a large error for a small signal. Drop it down to the mV range, and you get real again.
How tempting it is to search for every increasing digits /resolution in the belief that it gives you higher accuracy, and potentially makes you lazy when choosing the best range for your particular measurement.