In this paper, we propose a distributed coordinated constrained task execution (C2TE) algorithm that enables a team of vehicles from different lanes to cooperatively merge into an {\it ordering-flexible platoon} maneuvering on the desired lane. Therein, the platoon is flexible in the sense that no specific spatial ordering sequences of vehicles are predetermined. To attain such a flexible platoon, we first separate the multi-vehicle platoon (MVP) merging mission into two stages, namely, pre-merging regulation and {\it ordering-flexible platoon} merging, and then formulate them into distributed constraint-based optimization problems. Particularly, by encoding longitudinal-distance regulation and same-lane collision avoidance subtasks into the corresponding control barrier function (CBF) constraints, the proposed algorithm in Stage 1 can safely enlarge sufficient longitudinal distances among adjacent vehicles. Then, by encoding lateral convergence, longitudinal-target attraction, and neighboring collision avoidance subtasks into CBF constraints, the proposed algorithm in Stage~2 can efficiently achieve the {\it ordering-flexible platoon}. Note that the {\it ordering-flexible platoon} is realized through the interaction of the longitudinal-target attraction and time-varying neighboring collision avoidance constraints simultaneously. Feasibility guarantee and rigorous convergence analysis are both provided under strong nonlinear couplings induced by flexible orderings. Finally, experiments using three autonomous mobile vehicles (AMVs) are conducted to verify the effectiveness and flexibility of the proposed algorithm, and extensive simulations are performed to demonstrate its robustness, adaptability, and scalability when tackling vehicles' sudden breakdown, new appearing, different number of lanes, mixed autonomy, and large-scale scenarios, respectively.