When you fly around on the elytra with rockets (Any length of duration) and click to enter a mine cart, you can be rendered as still flying under the mine cart but still be "in" the mine cart. Make sure to click the bottom of the cart, and you'll see that it shows your character in the flying animation under the mine cart, while giving you the option of shift to leave mine cart. You cannot move the mine cart or fly away in this state, but you can shift to leave the cart.