In the 16th century if a writer mentions that soldiers were wearing "jacks" without any additional qualifiers, would that mean that they are referring exclusively to fabric armor, or did it become a general term for a wide variety of flexible armors, including mail and brigandine?

In general I've come to understand jack as referring to a flexible armor with a front closure, so depending on the time period in question it could be a variety of textile or flexible armor in various combinations.

That's always been my understanding. A 'jack' could be any number of things----a coat-of-plates, a gamboised shirt of mail, or even just a plain gambeson. The term's definition just depends on when and where you are. I may be all wrong about that, but I'll stick to it until someone proves different. :p .......McM

It is impossible to say that the gambeson declined because it isn't possible to clearly define what it was. Some texts use the term to describe underpadding for armour while others use the term to denote a standalone armour while others use it to denote part of a multi-layered defence.

We can say that the actual word declines in use but that just means that they started using different terms (such as "jack") to describe the above garments, not that the garments themselves stopped being used.

Regarding the original question, we run into the same problem. The term "jack" was used to denote all of the above garments. We can use a more specific definition today (such as "a flexible armor with a front closure") but that doesn't help us interpret contemporary texts.