Before embarking on a project like a chainmail brassiere, a number of factors must be considered. The first is the desired effect. If this is a garment meant to be worn on its own (ahem) merit, that is, without any cloth undergarment, serious consideration should be given to the material from which it is made. Most women find a 5-7lb steel bra a little uncomforatble. Unfortunately, because of the wieght of galvanized or stainless steel, any weave that would be sufficiently dense to adequetly cover important bits (as per local custom/laws), would also be impractical to wear. For this reason, there is no real choice except alluminum for such a garment. On the other hand, if this is something which will be worn over an existing cloth article, most metals will do as long as a loose weave is used. A little experimentation will help you decide what size and material rings to use. If you are unsure try calculating the amount of material it will take to make the bra (try measuring a favorite cloth brassiere). Then make a one inch square of material in the link size and material of your choice. Use a hand scale to determine the weight of your square and then extrapolate out to figure out the weight of the final piece.
This style of brassiere is primarily for those not looking for full support because it is based on the style of the famous (or infamous) "string bikini". It is recommended as a wear alone for small sized cups (A-B) or as a wear over for any size. It is also the simplest of the many different options because it involves only one shape.
Begin by making two identical triangles out of mail. These should not, however, be simple triangles (i.e. where every row decreases by one link). When triangles are made from mail in this way they will be far too short and wide for any practical wear. The best choice would be to start from the bottom and decrease the number of links in each row by one for every three rows. Since everybody has a different shape, it is best if frequent fittings can be made to ensure an exact fit. Just make sure that the mail is oriented in a vertical direction so that it opens when the sides are pulled.
There are a number of ways to construct the straps for the bra. I would not recommend making them out of chainmail because of the discomfort that this can cause when the straps dig into the skin on the sholders and back. The most practical straps are made out of lycra so that they can be stretched as in a normal bra. I have, however seen some interesting bras made with leather straps. I've been told that soft suede can be quite comfortable. For leather straps I would recommend puching holes and using metal reinforcements to connect with the mail. Lycra can be sewn directly to the mail. The strap that connect the tops of the two triangles together slips easily around the neck and the strap that connects the two inner corners should be fit from person to person. A connector of some sort will need to be added to the back of strap A, usually hooks and eyes or buttons. It should be noted that strap A can be made to be continuous and that the connector can be moved to the front, depending upon styles and tastes.