The Tazo Classic Chai Latte Concentrate is sweetened so no need to add any extra sugar, but if you do want it sweeter, add simple syrup since it'll mix in with the drink the best.
Not all chai concentrates are the same since every company makes their own chai blend using a range of different spices so stick with the Tazo brand if you want it to taste like the one at Starbucks.
You can add ice first, then the chai concentrate and the milk, but if you want it perfectly mixed without stirring, put the chai concentrate and milk in first, then the ice.
Starbucks uses 4 ingredients to make their Iced Chai Tea Latte in store: Tazo chai concentrate, water, milk, and ice. The Tazo chai concentrate used at Starbucks locations is made with less water so it's a lot more concentrated and stronger than the packaged Tazo chai concentrate sold in stores. They add extra water to dilute the chai concentrate when making the drink at the store.
Starbucks makes their iced chai latte with 2% milk but you can use any kind of milk you like, including oat and almond.
A delicious way to customize this drink is to add brown sugar syrup and swap 2% milk with oat milk. Top it off with Vanilla Sweet Cream Cold Foam.