Welcome to the site Jay!
One or both of the neoprene guides of the chain may be worn out or broken.
I would inspect those first.
With proper lubrication, that chain should be almost new.
Cam chains serving over 100K miles are not uncommon for the old generation of Ninja 250.
The automatic tensioner should be able to keep its position without backing up (and producing slack); that is the function of a properly lubricated ratcheting mechanism.
Measuring the actual path of the chain (rather than any slack) is the way to diagnostic its condition.
When the chain is really stretched out, the lever that the tensioner pushes reaches a point that hits the crankcase and no further adjustment is possible.
That is what I have learned from Mark Krieger, who makes a manual cam chain tensioner.
http://www.kriegercamchaintensioners.com/
The advantage of the manual tensioner is that the pressure of the OM spring-plunge is eliminated, and non-back up is a sure thing.
The only danger is over-tensing the chain or neglected periodic adjustment (every 5K miles or so).
I have heard that some people have cut the chain and ribetted a new chain (just like the secondary chain) instead of opening the engine for replacement; however, I don't know the details or results.
I would replace the cam and clutch sprockets together with the chain.