I was able to get mine working but only after searching through a ton of seller's descriptions until I finally found one that told me the trick. I basically guessed what it might be, but even the instructions from that seller weren't helpful because the solution they described didn't really exist on the bulk of the boards that I saw.
The tip said you could use a 'jumper to the right of the 2x4 connector to set the flash mode". The problem is, mine didn't have a jumper and doing a google image search didn't seem to find any with jumpers either, no less any more detailed descriptions of what it might entail.
The long and the short of it is that there is nothing in this device to properly set the flash mode, so you're left in the same position of having to create a low condition on GPIO0. I didn't bother running a full check of the wiring, but there are two tiny little solder points on the back which may well be tied to these pins. But the pins of the 2x4 coming through the board made for much bigger points to solder to, so I chose to attach to those instead.
Simply solder some kind of switch between the two (if you prefer, include a resistor inline with the switch for a more balanced connection) and then flip the switch to trigger the flash mode. (see second pic)
After that, I had no problem programming an ESP-01, the programmer is very low profile - no chords to deal with and the ESP-01 plugs directly into it. I use the Arduino IDE and it worked fine in there. They cost only a couple of bucks on ebay and make for a quick and easy way to program an '01 once you know that you still need to shunt the GPIO0 line.
I hope this saves someone the trouble I ran into! Have fun programming!
Example of one of the programmers
Back side of mine with GPIO0 switch installed: