I don't know about authenticating the fiber itself, but I'd just look for corresponding quality indicators in the jacket. Vicuna is so expensive I'd be really really skeptical if it wasn't A) a well-known high-end brand a la Oxxford, Kiton, etc. and/or B) obviously really well made, handsewn, etc.
Going to dissent here. If the piece is current, it will likely be one of the brands you mentioned...as I recall only Loro Piana has license to harvest the wool and you will likely see some indication of that.
However, you are more likely to find an older piece. I have found several vintage pieces, and most of the high end brands of today weren't around in the 50's-60's when vicuna was more prevalent.
Agree on the fact that the piece should be obviously well made. But the test for me is the feel of the fabric. Even a piece from the 50's should have an amazingly soft hand if it is 100% vicuna.