well, i can foresee a few problems with trying to do that..not saying that it won't work or is impossible, but.....
for one thing, you would have to weld a multi-speed cassette style sprocket to the hub on the left side.
you would have to find a different derailer, because a derailer is set up for right side chains only, if you flip it to the left, it will be backwards.
A bicycle chain is the only chain that would fit the derailer and bike rear sprockets, and a bike chain will not fit on the sprocket that's on the engine (on a happy time style engine anyway.)
if you did get it to work i would not be surprised if it threw the chain off when you shifted the gears, because the engine chain does not like any left- right variance...it must remain as true as possible.
when you shift, the derailer changes the angle of the chain to get it onto the different sprockets.
if you were going to try and do this, without a shifter kit, the only way possible that i can think of would be to find or make a left side drive hub with an internal 3 speed set up. or, get a standard 3 speed internal shifting hub, and weld the sprocket to the hub so it will rotate either way with the rim (get rid of the free wheel or coaster brake). but then again, you would have the problem of getting a chain that would fit both sprockets. a bicycle sprocket in the rear and a 415-410 chain size sprocket on the engine.
BUT, the other issue would be the gear ratio if you tried to make this work. it would be geared so high, that you would probably have 0 low end torque. a 10 tooth sprocket on the engine and a 19-20 tooth sprocket on the hub(or whatever size sprocket a 3 speed hub would have.) but also, i have no idea how low 1str gear is in a 3 speed hub...it may just work out to be fine.
another thought would be to use a 3 speed internal hub, and remove the bike sprocket. Weld a 41 tooth sprocket to the hub so it rotates both ways with the wheel. I have no idea if this would work or not, but then you would have the low end torque from the 41 tooth sprocket (in 1st gear) and then you would be able to shift 2-3 and maybe get some more top end out of it.
i have no idea how the internal 3 speed hubs are geared and it might not work the way i am thinking. a 41 btooth sprocket may be too big for the gearing in the hub, and even with 3 gears you may end up the same as if you just bolted a 41 tooth sprocket to a single speed hub.
it would take some experimenting with hubs, sprockets ands chains, and to figure out what size rear spreocket would work best with a 3 speed hub. you may have to drop to a 36 tooth rear sprocket because 1st gear in the 3 speed hub may be too low for a 41 tooth sprocket. and then again 3rd gear may not be high enough to give you the speed you are looking for if you try the 41 tooth sprocket.
I'm not saying that it can't be done...anything is possible with a little imagination, trial and error, and the willingness to make it work.