Can elven chainmail be made magical? If so, do any special rules apply? If not, where is it made clear that it can't be made magical?
Elven chain is just mithril chainmail with a +1000 gp cost to make it considered light armor for the purposes of proficiency. It is not itself magical nor is there any reason it could not be so enhanced.
To determine the final cost, use the listed cost of 5150 gp as the cost of the armor itself. For instance, a suit of +2 elven chain would be 9150 gp: 5150 (for the armor) + 4000 (for the +2 enhancement).
I can find no indication that Elven Chainmail cannot be magic-ed up, nor that any special rules would apply. Nor can I think of any reason that it should be so restricted.
Since it's mithril, note that it's already considered to be masterwork, so the attendant cost increase and armor check penalty reduction have already been factored in. I wouldn't call that a special rule so much as something that may get missed, though.