First thing to do on any newly acquired sled is to do a compression check. That will tell you if the pistons and rings and cylinders are in good shape. The main thing you want is that the reading on both cylinders are the same (within about 10%) and are above 110 PSI. you want to block the throttle wide open, remove both plugs, and keep getting a reading until it quits increasing, about 3 -5 pulls. Once you have that and it is reasonable, then start looking at crank seals... let me rephrase that... just replace them!! number one killer of Kawasaki motors is melted pistons from leaking crank seals!!
Won't solve your bog but it will make your sled last longer and it can be a long walk back t the trailer with a melted motor.
As for your bog, make sure the idle is set to 3,000 rpm, new belt, and clean out the primary clutch with some brake cleaner, NO OIL!! they are supposed to be dry inside. next, check to see that the carbs are pulling at the same time. They should both open at the same time, and have the same vacuum on each side. after all the adjustments, double check the oil injection cable adjustment. Make sure it opens at the same time as the carbs.
That should get you started. There are plenty of other things to check / adjust. we are here to help. the 340 sled is still one of my favorites as they take off much quicker and are just plain fun!!