How can I figure out if my store bought chlorine is the percentage it says it is? Chlorine is an important part of maintaining any pool. I've read horror stories of people buying chlorine from pool stores or big box stores and the chlorine being ineffective. 

If stored long enough Chlorine can degrade, lose it's strength. If put in the sun i've read that it can speed up that process. 

Like most pool owners, I have a pool test kit that tests how much chlorine is in a pool water sample. I specifically own a Taylor K-2006c Kit which test for Free Chlorine using the FAS-DPD Method. 

At most pool stores they supply 12.5% Sodium Hypochlorite and 87.5% Other Ingredients.

With my given test kit would it be possible to accurately test whether or not it's actually 12.5% Sodium Hypochlorite or not? If so, how would I go about doing so?

If not; What do you recommend using in order to test the chlorine.
Bleach solutions can be analyzed by addition of iodide and back titration with thiosulfite - somewhat difficult for non-laboratory conditions. Kits are available, but expensive (~$250).

A less precise (but probably adequate) method involves measuring the heat evolved as bleach oxidizes acetone. https://www.flinnsci.com/api/library/Download/650c3e8ed0574ed18c7b37b8832cccae It seems that you might be able to modify this process to do a rough quantification (+/- 10%) quickly. It was also discussed briefly on Quora: https://www.quora.com/When-happens-when-acetone-and-bleach-are-mixed

Just realize that if you drop solid hypochlorite into pure acetone, it could explode, catch fire, and make you wish you had never tried it. Creep up on this reaction: add only small amounts of acetone (1-2 grams) to a dilute hypochlorite solution (~5% ?) until you get the feel of how fast and how hot this reaction will go.

Eye protection is mandatory. Also have some water available (like a hose). Just be safe by expecting danger.