This paper contains two main features: a provably correct distributed control strategy for convergence of multiple nonholonomic agents to a desired feasible formation configuration and a connection between formation infeasibility and flocking behavior in nonholonomic kinematic multi-agent systems. In particular, it is shown that when inter-agent formation objectives cannot occur simultaneously in the state-space then, under certain assumptions, the agents velocity vectors and orientations converge to a common value at steady state, under the same control strategy that would lead to a feasible formation. Convergence guarantees are provided in both cases using tools form algebraic graph theory and Lyapunov analysis. The results are verified through computer simulations. This is an extension of a result established in our previous work for multiple holonomic kinematic agents.