You can get suitcases from the Lost and Found in the Oasis Lobby. Once you have tapped on the Lost and Found, you need to watch an ad to get a suitcase coupon. You can get up to 2 suitcase coupons this way. You then need to tap the big green button to pick your first loot box.

Once you open your first loot box, you can choose to pay 40 diamonds for each loot box you choose to open beyond the first. If you have more than 10 suitcase coupons, you can also choose to open them all at once!