Your Iron Flask’s powder-coating is the main reason why your tumbler can’t go inside your dishwasher. The entire process and high temperature are brutal on the coating.
Instead, gently brush your iron Flask and clean it using hot water with soap. Now, if you notice spots inside the bottle (stainless steel is rust-resistant anyway), you can put distilled vinegar and shake it for 10 minutes. If that extra effort still didn’t work, use water with baking soda while brushing.
The lids are safe to sit on your dishwasher’s top rack.