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 silver bell to pick your first loot box. If you have enough suitcase coupons to open 10 at a time, you can tap on the gold bell to open 10 suitcases at once.
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!