Ohh for heaves sakes hehehe ;-}
SickBikes 'Shift Kit' IS a jackshaft and nothing more, I keep trying to get them to change the name to avoid confusion.
It 'highJacks' the motors left side chain drive output and transfers it over to the right side of the bike via a 'Shaft', hence JackShaft.
The kit has 2 parts, the part you bolt to motor which has the rear dual motor mount and the shaft itself, the second part is a complete replacement of your bikes Bottom Bracket, the hole your pedal cranks go through.
That bottom bracket part has a special Freewheel pedal crank and arms and 2 sprockets.
The larger outside sprocket replaces your normal pedal sprocket that goes to your back wheel.
The inner smaller sprocket is driven by the chain and tiny sprocket on the end of the Jackshaft on the right side so you motor power goes to the same sprocket assembly as your pedals are using.
The 'magic part' is the freewheel crank on the right pedal that allows either you, the motor, or both power you back wheel.
Can you use a jackshaft on a single speed coaster brake bike?
Sure, but that would be an expensive waste of time.
The whole point is to use whatever gears the pedal side of the bike has so the motor can use them too!
Yes, derailleur gears work, internal hub shifters work, even NuVinci CVT hubs work, heck I have my 12th new shifter build here in the shop almost done, a Cadillac with a Jackshafted NuVinci that is just as sweet as ever ;-}
ANyway, about the 'gear reduction' stuff that has been said, between the 3 JS ratio changes it works out to be about the same for a JS to just a coaster bike with an 18 tooth sprocket as a standard kit direct drive with a 44T on the rear wheel, it is the underdrive and overdrive of your rear wheels system that makes the final ratio by gear selection at the time.
I hope that clears it up for you but I leave you with one important note...
If this is your first build and you are not a master mechanic with 2-stroke motor and bicycle skills I HIGHLY RECOMMEND YOU BUILD A STANDARD KIT FIRST!
This is not child's play, we are talking exacting complex mechanical parts transferring a huge amount of power on kit parts you need to assemble part by part yourself, and they don't go together like perfect lego blocks, nor do they stay that way if you don't do it perfect the first time.
Just a tip so you don't end up with a bike you finally get running only to have your drive train constantly fail.