Do I need a different chain if I change my gearing?
If you're just changing the front sprocket you don't need a different chain. In fact, you probably won't need anything other than a standard 520–106 for any of the most common sprocket combinations on the Ninja 250.
The main reason you would need to change chain sizes would be if you were to run out of adjustment range, meaning you reached the limit the rear axle can be moved in the slots in the swingarm. As a general rule of thumb you have to move the rear wheel about 1/8" for every tooth you add or remove. When you run out of adjustment you have to remove/add a pair of chain links.
The Ninja has about an inch and a quarter (or maybe a little more) of axle adjustment. Most of it is rearward, but there is enough forward for a 15T front.
The lowest gearing you're likely to use on the Ninja is 15/41, and, if you live anywhere close to any sort of hill, 15/42 will probably be as low as you want to go. Your stock chain will be fine for these applications, as well as the ones closer to the stock 14/45. The adjusters will be farther back is all. A 14/39 combination will necessitate a shorter chain, among other drawbacks.
Please see this article for information on the effects of different gearing.