Kanth,
In the Aces High III folder there is a file ahupload. Double click on it and you can upload the .mis file you created in the mission editor. Just check the box upload mission to host. When you create a custom arena with the terrain associated with that mission, it will then be in the staged mission list.
Edit Just tried custom arena in AHIII and no staged missions showed although they did show up in the melee arena (see post in dx11 bugs)