when chain is both tight & loose, is an indication that sprocket isn't centered in the up/down direction - loosen it up and spin it with a piece of wire or tape on the frame to point to the top of sprocket - at a high spot, put an old drill bit between teeth and smack it hard with a hammer until it is centered all the way around
A few things: please take more pictures of the INSIDE of the sprocket and one from the rear looking toward the engine so we can see the alignment. The rag-joint is not visible; this must be installed properly; have you "sandwiched" the spokes in the rags? Also, your sprocket is installed dish-in. You can flip it to make it dish-out, and gain about 1/4" clearance. Finally, your tensioner looks like it's fully extended. I recommend that you retract it and remove a link from your chain; re-tention accordingly.
Like Kioshk said, I think you will have to remove a link or two from your chain. It's very common to have to do this and I believe it's your main problem. Assuming that your rear sprocket is aligned properly and running straight and true.
Also keep in mind that your chain will "stretch" while you are breaking in the engine. After a couple of hundred miles it will stabilize in length so if yours is already too loose it will just get worse until the chain itself gets worn in.
Center the sprocket properly. Chain whip is ALWAYS due to too much slack at some point.
It happens under deceleration and at certain resonant frequencies under acceleration.
Another cause is the crappy chinese chain you get with typical kits.
Take a brand new chinese chain and bend it sideways: It will bend a LOT in a 1ft length
Take a good quality chain like Diamond/etc and it will not bend more than 1/2-3/4 inch per foot.
Most japanese companies suggest you replace a chain when it bends 3/4 per foot....
Chinese chains come NEW able to bend 6 inches or more per foot