I also have an Adams F2, a tall horn as was mentioned. It fits in my Cronkite triple trumpet case with one other horn, but it’s a bit tight. I wouldn’t travel with it, but it’s ok in my truck on the way to and from rehearsal.
I have a ProTec Flugelhorn/Trumpet case works very well with the Adams and either my Miyashiro or Committee and the risk of damage is a lot lower. It’s just not quite as easy to carry.
-the Chief Gearhead