I have a Canon A620 with an articulating screen - works well, was arguably the best camera at that price point a couple of years ago.
We just bought a "cheap" camera for the lab, a Nikon Coolpix L120. It will focus down to about 1/2" in macro mode with the lens set to wide angle - this means a postage stamp will fill most of the field. Downside is that when you focus that close, the edge of the lens barrel shades the flash, so unless there's plenty of ambient, lighting can be an issue. We haven't explored all the features and capabilities yet, but I used it to document a couple of teardowns of competitive products and it worked well . . . a colleague who shot a short internal training film with it said the HD video (720, not 1080) was "adequate." (No audio was required.)
Both of these cameras are a bigger than "pocket size" and neither one has the capability of a DSLR, but maybe something from the same family will work for you.