Looks like a really sturdy setup. Only thing I would've done differently is I wouldn't use such a tiny rear sprocket; it means there's a huge amount of torque pulling the axle forwards- wearing the right hub bearing extra fast and pulling on the bicycle chain super hard. If you used a larger rear sprocket (I'd go for ~36t), you could get away with less primary gear reduction (maybe even eliminate a jackshaft), while having a higher fraction of the chain tension going towards spinning the wheel (more leverage) vs. pulling the axle inwards.
I say this because I built a 5 speed bike with a 140cc 2-stroke lawnmower engine, and in 5th gear (3500rpm=around 40mph), when I look down the chain is moving at a ridiculously slow speed- like if I lug the engine I can follow a specific link with my eyes. Which means there's tons of axle/chain torque. My 5th gear sprocket is 15t- same as yours, but my wheel is 20" and I assume yours is a 26"... which is worse because more rotating torque is required.
Now I don't really think it will be much of a problem for you with the 79cc (2.5hp?) engine and centrifugal clutch. But my bike could do wheelies in first gear from idle without even popping the clutch, and had a top speed something like 60mph (don't want to test it and die/throw the rod/explode the flywheel since the engine is ungoverned). And if I was doing it again I would definitely go for larger rear sprockets, to take some strain off the components. I broke a brand new 3/32" Z-chain twice, each within 5 minutes. I've been having no problems with wide 1/8" chain however the side plates keep on shifting outwards on the pins (luckily the pins are extra long, unlike the flush-cut pins on the 3/32"). There's also 3 missing teeth on my 1st gear sprocket (not a problem), and I broke the rear freewheel twice before welding the sprockets directly to the hub. Some of these problems might've been more caused by my shifting system, but it just shows how much force there really was on that little bmx chain.
This is my chain/shifting setup, which would take 5 paragraphs complicated to explain lol. Basically all the extra tensioners/guides/etc. are needed because the rear cassette is welded right to the hub. It's extremely dangerous (the wheel locked up many times during the refinement stage)... I probably wouldn't do it this way again. I was also rushing when I was making it and I started it before I had a welder- so I was stuck with all these crappy no-welding-required designs.
here's the whole bike by the way
(end ramble) But like I said I don't think it will be a problem with your setup; or at least not any time soon. And I see that you're trying to make it with pre-existing components anyways. What you could do though, if it ever actually becomes a problem, is use a disk brake hub and bolt a larger sprocket to the disk brake flange.