Welcome to the forum, Ironcloud65! Sorry your first experience is frustrating. The Nitecore battery you got is a very good one but unfortunately just way too long. As mentioned above, “normal” factory cells are made to rather specific dimensions, and if aftermarket companies add things like tiny electronic protection circuits, button tops, usb charging boards, etc, then the length grows. If a flashlight is made to accommodate this, then good, but most are not and have a limited range of cell lengths that they can take. So you need a shorter cell.
The FT03 is a great light. It was mostly designed around 26650 cells - fatter and shorter than 21700. But it has just enough length inside when the springs at both ends of the tube are compressed that it can handle a standard 21700 also. That fit is pretty snug, however, and there just isn’t any extra room for cells with added stuff.
Two things to help you out a little. First is a link to Henrik’s excellent site where he tests lots of batteries for performance as well as chargers and other electronic gizmos. This is an article where he shows how a protected cell is put together. The visuals might make it easier to see why the Nitecore isn’t going to work.
Anatomy of a protected cell: The Anatomy of a Protected Battery
Disassembly of USB cell: Disassembly of USB charged batteries
Second is the numerical models of batteries. It’s all metric, and the cells are divided into two dimensions: diameter and length. So your 21700 cell - as a factory standard flat-top - will measure 21mm in diameter and 70mm in length. If you measure this yourself, eyeball it with a ruler but do not use metal slide calipers that will conduct electricity! Protect the jaws or use plastic/nylon ones…else sparks will fly and hopefully no more than that. 
So that gives us a 21 and a 70….but an extra zero on the end. You can ignore that zero…theoretically it means that it’s designated as a round cell shape but I guess there was some debate about that (and at any rate you never see anything else on cells).
So….a 26650 which your light can also use and was mostly designed around, measures about 26mm in diameter and 65mm in length. Those are somewhere between a C and D cell, sizewise. Putting the 21700 cell in there means you need some kind of spacer so the skinnier cell doesn’t rattle (it should have come with a plastic tube….although mine back in the day came with one to fit the smaller 18650…not sure what they sell now). And then the extra length hopefully fits in the tube body when the springs are further squished.
I only have one protected 21700 cell and it measures 75.3mm. It will not fit in the FT03 - no way, no how. If you were to try extra hard to force the cap into starting to thread on the tube, it’s likely that one or both ends of that longer cell would get dented in (and that’s bad). All of my normal standard 21700 cells measure spot on 70mm or just a hair longer….they all fit but it’s snug and it takes a little more effort to start the tail cap than it does with the shorter 26650 in there. So….you need a standard flat-top cell for this light.
I don’t think Nitecore sells any standard cells as they have really shifted toward protected cells - often those will only add 3mm by themselves (i.e. no usb charging board added) but that’ll still be too long. So don’t let them encourage you to try another of their cells for your light. If you can get a refund on yours, that’d be great.
Here are some links from good respected suppliers for 21700 cells. It’s not super important as far as which one you choose for this light. Some have 4000mAh or 4200mAh capacity (which mostly equals run time) and some have 5000mAh. There’s a tradeoff between them for performance in some lights, but for the FT03 any will be ok really. I’ll link a few and you can compare pricing between sites. The Molicel brand has excellent ones, as do the big brands like Samsung and LG. Vapcell is a rewrapping company who doesn’t manufacture anything themselves, but they generally have great cells also (and some excellent ones). Compare total price with shipping…pick up a couple. Don’t bother with Amazon for these, though…they have shied away from loose lithium-ion cells and the ones they do still have are usually sub-par.
Aloft Hobbies: super nice folks, mostly hobby/RC instead of flashlights…decent prices but super cheap and fast shipping. Samsung 40T is the only 21700 they sell…it’s excellent: https://alofthobbies.com/inr21700-40t-4000mah-li-ion-flat-top-battery.html
Liion Wholesale: one of the best places, super price on the Molicel P42 - they’re a little low on stock right now with global conditions but they have some others to look at, too: Molicel/NPE INR-21700-P42A 4200mAh 21700 Battery - Authorized Dealer – Liion Wholesale Batteries
Illumn: great folks, used to be here on the forum a lot, reasonable with pricing and shipping, here’s the Samsung 50E which has more capacity than the 40T above, and still can handle what the FT03 asks of it: https://www.illumn.com/batteries-chargers-and-powerpax-carriers/batteries/21700-samsung-inr2170050e-5000mah-high-discharge-flat-top.html
IMR Batteries: great prices but they make you buy at least 2 at a time…they seem to have a lot in stock at the moment so here are a few links:
Samsung 50E: Samsung 50E 21700 5000mAh 9.8A Battery
Samsung 40T: Samsung 40T 21700 4000mAh 35A Battery
Molicel P42: Molicel P42A 21700 4200mAh 45A Battery | INR-21700-P42A
And since the FT03 has built in onboard charging, you definitely do not need a cell that has that feature. Good old normal battery and a usb cable and you’re all set. If you want to get a normal separate li-ion battery charger, most of us prefer those for various reasons but the charging circuit in this flashlight is good and dependable, so no real need.
Wall of text and links but I hope this helps you. I think you’ll love that light. Kinda large but it’s impressive and easy to use…still one of my favorites.
(and a side note, there’s another muuuch larger battery available if you ever decide you want a lot longer run time from this light on high (or in any mode). Those are 26800 cells. You have to order the longer battery tube for the light from Banggood for around $10 with a coupon (on this site), and then the bigger cells are available from Aloft Hobbies. They’re really impressive…adds weight and length, though.)
