You must get all 200 7th Legion Service Medals on a single character since you cannot trade these between your characters.
When you have 200 x 7th Legion Service Medals, buy the mount from Provisioner Stoutforge. When you learn it, it can be used by any Alliance character on your Blizzard account.
How to get 200 7th Legion Service MedalsYou get 7th Legion Service Medals in four different ways right now:
1) Complete the Warfront win quest. Each Warfront cycle each of your characters will get a quest to win the Warfront, and this quest awards 15 x 7th Legion Service Medals along with a piece of high ilvl gear.
2) Win Faction Assaults. These will happen roughly once per day (or more like every 18 hours), and "winning" on by doing 4 World Quests followed by a short regular quest gives you 5 x 7th Legion Service Medals.
3) Complete Warfront zone World Quests. When the Alliance controls a Warfront zone, you get access to 5 World Quests that reset daily. Each of these award one Service Medal each, so you can get 5 x 7th Legion Service Medals per day per zone that the Alliance controls.
4) Open 7th Legion Paragon Caches. After you reach Exalted with the 7th Legion, you begin to gain Paragon Reputation, which gives you a Paragon Cache after every 10k rep obtained with them. This cache includes some nice stuff, including 25x 7th legion Service Medals. You won't get these too often tough, but they are a nice bonus when you get one.
As you can see, there are not many sources of the 7th Legion Service Medals, and most of them are gated behind daily or weekly cycles, making it difficult to grind all the 200 Service Medals needed in a short time. I would expect that most people use between 2 and 3 weeks of daily or close to daily farming to get this mount, so be prepared to spend some time on getting the Azureshell Krolusk.