This design is Very similar to the Poppin hot air engine I built. I am no expert, but I will share a few pointers.
First, these engines are quite low power, so Anything you can do to make them spin freely is benifical!
I see a drip oiler on this unit, some use mineral oil or similar...but I have found dry graphite to work better IMHO...if there is old burnt oil residue inside the cyl it "could" be part of the problem. I might suggest removing the head and piston and give a good cleaning, then I lube the bore and piston with pencil graphite, I like pencil because you can "color" the bore verse graphite powder sometimes has larger particles that can be a problem...really high grade graphite is finer than bread flour with no large particles and if you have that, then fine to use. Next reinstall piston and spin the flywheel, it should coast several times around with no head to make compression...if it does not? Investigate why.
If all is well, clean and install head.
Perhaps stone or Flat polish the valve you made on fine sandpaper and flat surface, (side that touches head)the polish will remove burrs and high spots and the polish marks will tell you if it really is flat. Also inspect the head where the valve rubs and flat polish on fine sandpaper if needed.
There probably is some adjustment on the jam nuts that hold the slide valve on, the slide valve should have light spring tension but not so much as to pull the valve away from the head on one side. It must sit flat and seal.
If you get this far, check that the valve is completely uncover the hole on down stroke and completely cover the hole on the up stroke.
Oil the crank and piston wrist pin, now completely assembled you should feel a bit of compression or vacuum resistance when spinning the flywheel by hand if your valve is working and the timing is correct.
Try it with 100% Alcohol if you can get it? Rubbing alcohol contains water and you don't really want water in your bore.
Let's us know how it goes? If the engine try's a little but still does not run, perhaps you could post a video and we can offer more suggestions...good luck!... Little improvements count here
PS: I find thinner valve stock is best, these slide valves do leak some and so the engine runs on vacuum but a leaky slide valve may let in enough (cool) air that the engine makes a little compression near the top dead center if to much air got in cyl....the thin valve stock can flex away from head to release any positive pressure but snap back to seal for vacuum air next cycle. We want only very hot and very dry air to be drawn in when the valve is open, then as little leaking as possible when the valve covers the hole.