The jet packs were given to the girls by The Wise Man in the final tier of their journey, in the train realm. The Wise Man explained the mission to the girls, they were obtain a bomb code-named 'Kitchen Knife', and they were to use the jet packs to escape the train.
After killing several robots, they were seconds from taking the bomb out of the train, and Rocket and Sweet Pea had put on their jet pack. A robot had awakened and throws Rocket against the wall, causing her jet pack to break, and he armed the bomb. Rocket's jet pack was broken, she knew her sister's jetpack wouldn't be able to carry both of them, so she activated Sweet Pea's jetpack to send her away from the train. Rocket remained behind as the train arrived at the city and the bomb detonated, killing her and destroying the city.