Mounts in Lost Ark rarely give out any real benefits compared to the base mounts you get when just starting the game. In MMOs, though, the prestige of having a special mount is reward enough though.
Lost Ark is a game that is all about its gear scores. When it comes to claiming the Chamkuri mount, it's no different. To claim the mount, you must have a gear score of, at the minimum, 460, meaning that you had to have already completed the Shushire Questline.
The Questline to get the Dawn Chamkuri mount begins in Rohendel, meaning that is your first stop. once there, around the middle of the Questline, you will have the opportunity to meet a wizard named Digne. The NPC Wizard Digne will award you the Dawn Chamkuri mount.
If, on the other hand, you are looking to get the Chamkuri mount as a login reward, the process is even simpler, merely redeem a box containing one of the available Chamkuri mounts.
Unfortunately, there is no in-game preview when redeeming these boxes as to what the mounts look like. Your best option, then, is to either enter the game and go to the major city centers to take a look at what all the Chamkuri mount options are, or scour the internet.
Luckily, you are not the only one being frustrated over this simple oversight. So, to combat this Western players have posted all the available options at their own expense, so you can make an informed choice.