Battery showing lightning indicator but percentage doesnt change.

Right, I've spoken to the seller and he is sending another battery to me. He claims that if this battery doesnt work then surely it is a problem with my phone instead. So is that even possible ? For an iPhone to somehow reject a replacement battery ?

Place a test (known good) battery in your iPhone (your old original battery in this case), let your phone drain it and shut off on its own. Then charge the iPhone using a known good wall charger and known good cable. If after ~10 minutes, the iPhone restarts and the battery level is showing 1%-4%, there is nothing wrong with your iPhone. Don't let them tell you otherwise.

RULE OF THUMB: starting at 1% means the battery is somewhat in bad shape. Starting at 4% means the opposite.

You ask if it is possible that an iPhone would "reject" a battery. Well a battery is made of "power cells" and a small control board. Either or both could be at fault and cause a multitude of funny symptoms. You must also know that the rate of defect is so high when it comes to replacement smartphone batteries, that I like to actually say that from time to time, we may come by a few good quality batteries. I'm not sure if that's just because of (very) poor manufacturing or planned (too well) obsolescence. Stick to reputed sellers who are eager to safeguard their reputation and will not shy away from their warranty, if any. Stay away from Amazon and eBay sellers. Not because all of them are bad, rather because you won't be able to tell the difference and the hit-and-miss rate will put you out of too much time and money.

Unfortunately, I dont possess any "good" batteries. While my original battery does charge, it is unable to hold them for long. I have to keep it plugged in and charging to use it for anything heavy. I remember running a test that shows the battery only having 100 mAh capacity remaining compared to the original 1440. I've been using the phone for approximately 2 years and according to Apple, the battery should still only degrade till 80% after that amount of time. The full charges cycle were also approximately 750-ish. Either I've been using my phone A LOT or something went very wrong or unlucky for me.

There are very little dealers for iPhone parts where I live. Even then, none of them are big stores that inspires confidence when you go for repairs. Not to mention that it will cost me 10% of my iPhone 5's original price for a full repair and replacement. Hence, my decision to fix it myself.

I'll post another update here when the new battery comes.