Don't.
I get it. You grew up reading fantasy novels or fighting orcs in your dreams and just learned that there are people out there making chainmail shirts and you want in on the fun. Believe me no one wants you to make a chainmail shirt more than me. So why am I discouraging you from making one? Because my first shirt took several years and is a disaster that I keep in a storage container because its ugly, it stinks (it really smells bad), and its unwearable. With a few suggestions I'm hoping you'll avoid making the same mistakes as me.
My early chainmail shirt project started when I was about 15 and lasted until I was about 22 where I managed to take a mile or two of galvanized fencing wire and turn it into a dull, smelly, unwearable sheet of chainmail fabric. In my enthusiasm I had decided to use European 6 in 1 weave to make my shirt and the ring size did not allow for flexibility or adding much in the way of sleeves without tearing itself apart. This decision had made my shirt ridiculously heavy and I was unable to remove it without assistance.
I had also decided to make my own rings as well for this project clipping each one by hand and then weaving them in to my heavy metal disaster. I started with a drill, a mandrel, and some galvanized steel fencing wire and churned out about 60k rings resulting in a lot of wasted time and effort. Cutting the rings alone took as much time as weaving all of them into my "shirt." For starters there are a lot of better materials commercially available for making rings other than galvanized steel. You can order wire in a variety of sizes and materials, from aluminum to gold, and use a drill and a mandrel to make your own rings that don't stink. There are also a ton of manufacturers of rings specifically made for chainmail. So you have to conduct a cost/benefit analysis of making your own rings vs ordering them. I'll be ordering my own rings from now on as there are people dedicated to making really high quality rings that are much better than anything I could make when I started, or even today.
Now, before I go on trashing galvanized steel let me clarify some things. There is no way to get rid of the smell but that doesn't mean you can't make a beautiful, shiny, wearable chainmail shirt out of it. If you use a tumbling process to shine up your rings and a better cutting process than hand cutting (like using machine cut or saw cut rings) and choosing a more flexible weave you can make some really nice rings and a very nice shirt.
Another mistake I made early on was choosing such a massive project. When you're starting out in sales your mentor should help you with that easy sale to help you get that sweet dopamine fix quickly, or when you're paying off debt its best to pay off your smallest debt first so that when you pay it off quickly you see that paying off your debt is achievable when taken one bite at a time. It's the same with handmade items. Small quick projects can quickly turn into easy wins giving you the capability and endurance to complete larger projects in a more timely manner than the 7 years it took for me to finish this one shirt. I spent a lot of time being burned out and not even wanting to finish it when I could have been hammering out much higher quality projects in a shorter amount of time.
I ended up "finishing" this shirt only when I had nothing else to do. I was deployed to Iraq at the time and while there was a lot of work there really wasn't much in the way of entertainment during your time off. I had ordered a roll of 14 gauge galvanized steel wire from theringlord.com, a drill and a mandrel and wanted to finish my shirt. It was then that I discovered the difference between Standard Wire Gauge (SWG), and American Wire Gauge (AWG). The roll of wire from TRL was larger in diameter than the wire I had started with from home depot. This mistake was pretty costly as I had ordered a half mile of wire that I still have to this day. It sits in my garage, smelling, by itself and every now and them I cut a piece off to use is a random project like wreath hanging during Christmas or hanging bird houses from the trees. After posting about my situation online someone came to my rescue and ended up sending me a roll of wire matching what I had bought at home depot. So now I had everything I needed to finish my project and I spent the majority of my deployment cutting rings and weaving them during my free time.
Once I completed this disaster of a chainmail shirt and had found TRL and other ring manufacturers I went on to complete hundreds of finished projects and about a million rings worth of chainmail. My production level went into high gear and the absolute quality of my work was through the roof. I was loving chainmail again and really enjoying my work and selling it.
I haven't included all my mistakes but I've pointed out the big ones for this shirt and now hopefully you can avoid them by doing a bit of research and making a plan. Get yourself a few small wins when you're starting out. Wallet chains, necklaces, and bracelets can be really fun and quick projects to make. Don't wear your enthusiasm down by cutting a ton of rings for one massive project. Get your birthday money and buy a few rings from a supplier and try them out. Make sure you understand the difference between SWG and AWG wire sizes before you order as it will effect everything. You're going to spend a lot of time and energy making a shirt and everything you do to make sure you create a quality project will pay off once you complete it.
If you find yourself burning out on a project or weaving becomes physically painful, stop and take a break. Let your body heal before you injure yourself permanently and make something else for awhile. Shirts are large time consuming projects and take a physical toll on your body. There's no sense injuring yourself and not being able to finish your project.
If you've made it to the end happy weaving. I look forward to the projects you will make!