Arne Koets shows an optimal configuration for a well-tailored suit of mail – close-fitting in the arms, somewhat looser in the body. This is admittedly a rather extreme example in terms of how precisely it is tailored to the individual wearer, but the general theme of close-fitting arms and more ease in the body is fairly consistent in most medieval European illustrations of mail.
A common problem with mail/chainmail is that there’s a real shortage of references of actually well fitting/well tailored outfits. To a certain extent, it’s fairly realistic that regular soldiers would not have had personally tailored armor – but it’s also led depictions of everything from billowy sleeves to practically painted on in what’s (supposedly) serious attempts to depict the armor.
As you can see, the fitting isn’t really that different to many other more conventional garments. The main thing to remember that you really can’t go much tighter than this because the mail will start to become less effective, and wearing it may actually harm you.