If you move the mouse cursor back down to the bottom bar, in the campaign menus, it will exit the current screen you're on (Loadout screen for example) so if you haven't confirmed the selection, it probably didn't work since you exited before doing so.
It took me a few head scratches to figure out why some of the campaign menus would exit back to the main one with the map, when I first started playing. Eventually figured out that moving the mouse down below would do that. It's nice not having to click the 'Done' button all those extra times but can be confusing at first until you know what's up.
I selected the JASTA 3 - 1916 skin and then clicked the 'TICK' to confirm, however there is no other way to get out of the briefing screen other than moving the cursor down to the bottom panel to select head to field / proceed to mission...
I don't understand it, it worked the first time I tried it and yet there seems to have been a glitch that wont allow aircraft skins to work in the mission......bloody frustrating!