Once all of my rings are cut and cleaned (22 links/inch of finished chain) I begin to fit the edges together for fusing. Fusing unfortunately doesn't work with every metal. Therefore I no longer make chain with less than 18K gold and standard Sterling won't fuse either. I have found that Argentium Silver works wonderfully and makes a splendid chain.
I highly recommend fusing instead of soldering the rings for a number of reasons. First, it's faster. Much. Second, it's stronger and more trustworthy. I once made a neck chain for a friend of mine in the jewelry business. Unbeknown to me, he was in the habit of putting his chain into an ultrasonic cleaner every night so that he would have the cleanest chain in town. About a year later he complained to me that it had some broken links. Upon examination that actually proved to be almost every link. The solder holding every single link together in a 20 inch chain had been completely broken down by the ultrasound.
Each link now has to be adjusted so that the ends butt together as tightly as possible for a sound fusion. They are then laid out on a flat surface, I use a steel anvil plate for convenience, and a touch of gold flux is applied to each joint. Using a number three torch tip for my small torch, I pick up each link with a fine tip hemostat and fuse the ends together. Some melt away but that's the way it goes. I usually don't lose more than about 5 % of my links using this method. I use to solder them whilst flat but that failed far too often. Fusion happens in the blink of an eye so a fast hand is needed. All of the now fused rings are pickled clean in a standard sparex solution and washed clean.
The next process of stretching the circular rings into long ovals has a nice by product of culling insufficiently fused pieces from out the herd. I use a dedicated pair of needle nose or chain nose pliers which I modified for this process. I filed small grooves into the tips of the pliers so the links would have a standard seat giving each one an identical profile. This is most important. Any deviation in the shape of the formed links will give rise to mounting inconsistencies in the finished chain which is unacceptable. The link is gripped on the tips of the pliers with the fusion joint at the twelve o'clock position. This assures that the joint will be positioned in the middle of the now oval link which puts the joint in the middle of the chain where it will remain unobtrusive. Each ring is gently spread outward giving it a flat oval form. The wire should only be pulled enough to form it, not to stretch it, which again would differ the one link from the rest. This is the point where badly fused links will tend to break and usually in a dramatic fashion. The ring will be on the tip of the pliers one moment and gone the next. Eye protection is always a great idea.
I use a small clip-on loupe through which I watch all steps of the chain-making process. Quality control must be an unblinking eye. Another 5 % of all links make me suspicious of the integrity of the joint. The fused joint has a slight haziness to it for lack of a better term. Even rings which passed the spreading stage can still be suspect. There are not many moments in Goldsmithing worse than finishing a beautiful new chain and finding broken links inside it. No good repair is possible. If for no other reason than peace of mind, suspect links are set aside to be used in other phases of the job. One of those phases is the next.