Well there's a good place to start, the vertical chain (large gear) is outside, furthest from the motor, but that doesn't explain why it's not turning, it shouldn't matter unless you are making the chains grab as far as starting goes..
A quarter inch like only one side and it's hard to get the flex? It should feel similar to a guitar string, flexible but tensioned well. If you are able to pedal the bike rather easily without grinding or odd sounds with the clutch pulled in then the chain slack should be OK.
Pull the spark plug out, and leave the clutch engaged to the wheel, roll the whole bike backwards 10 feet. If it won't roll then it's jammed somewhere, if it rolls but feels like it hit a wall then it's also jammed...
Try lifting the rear wheel and pedal the pedals forward without the plug in the head as well. If you have a leaky carb and your bottom end filled with gas it will become very hard to pedal untill it's cleared.
Keep us updated, I recommend swapping the chain rings out so the larger is on the outside. Apparently the further out the chain the less twist force the kit has to fight. I would also assume side loading the chain become more of a problem if the wheel chain is too far out (unless it's a single speed or internal gear hub, in which case it might not matter too much, but still getting the best alignment possible will give you the longest life from the gear and chain work.
