I would pack them the same what they do to ship them. Maybe bare root, stake the taller ones or spikes and wrap them snugly with paper and tape with masking tape. You might also want to consider boxing them if you suitcase is not hard sided.
I can't speak for FedEx or UPS, but I know that packages for the USPS, unless special handling is specifically paid for, are not handled gently and sorting is often automated. I, as a carrier, do try to handle my customer's packages with care, though I am human and sometimes drop packages or have them fall out of my car. The guys at the sorting facilities though... I have no doubt that they throw things around like luggage gets tossed around at the airport. They also will stack 40+ lb boxes on top of smaller things, even those with "fragile" plastered all over.
So, to my story, most of the packing I see to ship orchids keeps them safe, even if the box gets a bit beat up. I cannot imagine that airline luggage gets treated any worse than packages, and it is where I would start.
Here's a video on youtube from Kawamoto Orchids that might be useful for an idea on how to pack them.