Cobra Tricep Putter: Banned or not?

The club is fine.  Use it all you want.  Having the club in contact with your body above the elbow isn't allowed as I understand it.  Kuchar only runs it up his forearm.

It isn't the putter which would be disallowed, only the method with which it might be used.  If your method of anchoring it in your triceps also includes locking the upper arm to the body creating an anchored pivot, then I'm thinking that it would not be permitted.  That would amount to moving the pivot point a couple of inches but not effectively changing anything from the standard broomstick position against the chest.  The whole point of the rule change is to require that the part of the body controlling the club (the hands and forearms) not be anchored to the torso, so that the player makes a conventional stroke rather than a hinged pivot.  Locking the upper arm to the torso, then anchoring the club against that would be seen as trying to circumvent the rule without actually changing your stroke.

This is of course my opinion based on how you described your stroke.  Not seeing what you actually do, I can't be certain of anything.

http://www.usga.org/Rule-Books/Rules-of-Golf/Appendix-II/

The most relevant in there appears to be c, but I see nothing here which would make the putter illegal. I would make sure the lie angle is no greater than 80°.

c. Attachment to Clubhead

The shaft must be attached to the clubhead at the heel either directly or through a single plain neck and/or socket. The length from the top of the neck and/or socket to the sole of the club must not exceed 5 inches (127 mm), measured along the axis of, and following any bend in, the neck and/or socket (see Fig. VI).

Exception for Putters: The shaft or neck or socket of a putter may be fixed at any point in the head.