To destroy a ship to 70% you must first book a ship from the PC in your home shack.
Note: To get the 'Destroy % of the ship ____' achievements, you must do it in one 'docking'. i.e, you cannot dismiss the ship and bring it back on another day. Doing this will reset your progress for that ship. This means that you must have enough money in daily 'payments' to keep the ship docked until you've reached the desired percentage for the achievements.
The Flame ship is a medium-sized grey ship with 'SCS Shipping Line' on the side of it in big white letters.