I have not yet built a flame eater or vacuum engine, but I did do a little research on them to see if I could help you out. Vacuum engines such as this generate very little power, and most of them are capable of running themselves, and not much if anything else. With engines that generate so little power, there are two things that make all the difference: friction and leaks.
Bearing friction: Ball bearings on the crankshaft should help quite a bit. As you indicated, your instructions call for a very free running design. To achieve that, you need to be sure that your bearings are installed in perfect alignment with each other, any misalignment will cause lots of drag.
Piston fit (friction and leaks): Your piston must also be a close fit, but friction free, difficult but not impossible to achieve. You are looking for a piston to cylinder clearance of about .0005" which takes some patience to achieve. Once the piston fit is down to being a bit snug, but still movable, you need to lap it in to a proper fit. A good way to test for this is to set the cylinder vertically, then drop the piston into the bore. The piston should slowly drop all the way in on its own. If it stops, it is too tight. If it drops in quickly, it is too loose.
Valve fit (leaks): Make sure that you lap the valve to the cylinder as this needs to seal completely. If it leaks at all, even the tiniest amount, your engine will not run. Judging from the machining marks at the valve hole, showing in the photo, the valve has not been lapped in, and it will leak.
I see that the design and shape of the connecting rod can have a great effect on your valve timing, as can the length of the valve rod. An engine like this will also only run in one direction as the timing is incorrect if you try to run it the wrong direction. Some of these engines also run better once they have fully warmed up. You might try spinning the engine with a drill while the flame is present to get it warmed up. This occurs because in some engines, especially if the piston and cylinder are made of different materials, they expand at different rates, causing the piston to tighten up a bit in the bore. If it runs for a while then stops, the piston is just a shade too tight as it starts to bind when it warms up. If you can spin it with a drill to warm it up, and it runs on its own after that, it indicates that the piston is just a hair bit too small and it leaks too much until it warms up and expands.
Another recommendation that I stumbled on is to make the piston out of graphite. It is easy to machine and can be purchased on eBay or from McMaster Carr. It is also self lubricating.
I don't have much else, I hope these tidbits are helpful.
UPDATE: I just stumbled on the plans you used, from Jan Ridders. I was incorrect in the way I thought this particular engine works, but I can see now where there are a number of areas where leaks can occur, and I suspect this may be where you are running into problems. I can also see where this engine will run in either direction as well.