if the frame is not design for 20" wheel, you will get some issues with the brakes.

you could start from a children mtb like frog 52/55 or equivalent. then either you fit a steerer extension or a new uncut fork or a BMX handle bar. Your main issue will be the saddle/seat post. they are usually 27.2 when foldinding bikes tend to use 33.4.
My S-work seatpost is 350mm long and requires 100mm minimun insertion so, 250mm max protusion. If I was to fit that on the kid frog 52, it would be borderline safe and still too small for me.

Like jfouellette, I have a Frankenstein Smooth hound X9 (2008 frame, 2010 fork and many bits from the part bin) and built a hammerhead 8 D7 for my mother. In both cases, I started with a frameset and then fitted standard parts found either on 20" foldingbike or road/hybrid bike. Cost was low (£800 for mine, £400 for my mother's). As others said, if you ready want a minivelo, bit the bullet and commit to a frameset.