Link mechanisms, including Stephenson II link mechanisms for multi-position flaps and associated systems and methods are disclosed. A system in accordance with a particular embodiment includes an airfoil having an external flow surface with an upper portion and a lower portion, and with the airfoil forming a base link. The system further includes a six-bar linkage coupled to the airfoil and having a Stephenson II configuration, including a binary second link pivotably connected to the airfoil, a ternary third link pivotably connected to the second link, a binary fourth link pivotably connected to the third link, a ternary fifth link pivotably connected to the airfoil and the fourth link, and a binary sixth link pivotably connected to the third link and the fifth link. The system can further include a deployable leading edge panel carried by the linkage, with the leading edge panel being movable via the linkage between a stowed position and at least one deployed position.