Atmospheric pressure plasma jets (APPJs) have potential applications in many aspects ranging from traditional surface treatment to growing biomedicine. An array structure of such APPJs is the most efficient way to enlarge the treatment area. Nevertheless, the majority of APPJ arrays have shown mottled patterns downstream, a disadvantage for applications. Particularly, in biomedicine and certain other areas, improving the plasma homogeneity downstream of APPJ arrays is crucially needed. In this work, we numerically study synergistic effects of APPJ arrays on plasma propagation and homogeneity downstream based on a model coupling electric, flow, and temperature fields. Taking a two-dimensional three-tube APPJ array as an example, we study the influence of gas velocity and component, as well as applied voltages on plasma distributions. In addition, essential strategies for merging plasma bullets are acquired. Results show that the ionization rate between adjacent jets is important to provide electrons for jet merging. The helium mole fraction controls the plasma distribution and thus directly decides whether adjacent jets merge. After merging, the plasma bullets affect each other through the electric field to control the homogeneity downstream. Therefore, the plasma distribution is a result of the synergy of flow and electric fields. Then, a homogeneous plasma distribution downstream can be realized by the fine control of both fields, which provides an effective way to uniform the plasma downstream in plasma processing.