Double Clan XP activates automatically as soon as you reach the level. Basically once you get it your clan will have 2 hours Double Clan XP. I'm pretty sure every group of clan members who plays and earns during the Double XP "ticks" off time off the 2 hour counter. It will show on your clan details in the barracks the Double XP icon and how much time you have left. My clan is currently Level 9 so I've only done it once. When we earned it, we only had one 4 member party active at the time and made sure to play for the entire 2 hours and it worked for us whole time! Will update once we hit Level 10 and try it again! Good luck!
Usually the In-game Barracks Clan Details take a while to update. The Call of Duty App loads much faster and so far seems more reliable. Sure way to tell if you're earning Double XP still is to refresh your "My Clan" in the App 30 seconds or so after every match, compare your new total, a little math, and you should be able to tell pretty easily. All the regular amounts are listed in the original post! The best bet is to conserve your Double XP by only playing when you have (4) members available to play in the clan vs clan playlist, 800 XP per win and 160 XP per loss!
Figured instead of posting as a response to posters asking questions just to make a thread, hopefully make it easier for the community to find out about Clan XP & Rewards due to the lack of info out there. Nothing against yours, I think you did an amazing job with the screen caps of each reward! Anyways, I just wanted to make an easy to understand "condensed" list for those looking for information about Clan XP & Rewards! Something fellow clan leaders could simply copy/paste for use in their own websites & forums!