Future civil aircrafts require simple, low-noise, and highly efficient trailing-edge flaps. In this study, a detailed numerical study for flap improvements using steady and unsteady Reynolds-averaged Navier-Stokes computations was conducted. A movable trailing edge (MTE) was applied to the main element as a passive flow control method to improve the traditional Fowler flap. A new concept of a backward seamless flap (BSLF) based on the MTE configuration is proposed, which can eliminate external fairings, simplify the mechanisms, and reduce the cruise drag. Then, a wall jet active flow control method was used to improve the BSLF. The improvement effect, flow mechanism, and parameter influences were investigated in detail. The results indicated that the MTE can increase the lift coefficient in the linear segment by 1.2-1.4 for an aerofoil and 0.79 for a wing by controlling the slot flow, energy distribution, and circulation. Moreover, the BSLF provided an improvement in performance higher than 27% over the plain flap, and the wall jet controlled BSLF configuration could reach or even exceed the MTE configuration in terms of performance. The zero-mass jet had a higher control effect and efficiency than the continuous jet. This study highlighted the significance and engineering value for technical improvement and concept exploration of new-generation high-lift devices.