You can speak the carpet's command word as an action to make the carpet hover and fly. It moves according to your spoken directions, provided that you are within 30 feet of it.
This carpet is 6 feet by 9 feet and has a flying speed of 30 feet. It can carry up to 1,600 pounds, but its flying speed becomes 15 feet while carrying over 800 pounds.
Notes: Set: Speed (Flying), Movement, Utility, Exploration
The characters in my group weigh 891 pounds. With their inventory, 1,581 pounds.
They will fly, but they have to do it day and night to reach a relevant distance.