This article considers the problem of high-speed maneuvering target detection for a frequency diverse array (FDA) sensor in the presence of dense false target jamming (DFTJ). Different from conventional intrachannel coherent integration that only accumulates target signal within single channel, the FDA radar employs joint intrachannel and interchannel integrations to enhance the detection. Nevertheless, the challenges arise in that the target's high speed and maneuverability lead to the range migration (RM) and Doppler frequency migration (DFM) within each channel. Besides, due to the coupling between the frequency offset and the target velocity, Doppler frequency spread (DFS) occurs across the channels, which results in severe gain degradation in interchannel integration. Moreover, the detection may suffer from serious performance loss under the DFTJ. To tackle these issues, a systematic methodology is proposed for multichannel coherent integration based on an FDA radar. By exploiting the features of the DFTJ signal in the range-frequency domain, an image filtering process (IFP) is proposed to eliminate the DFTJ while preserving the target signal. On this basis, a modified Keystone transform (MKT) as well as phase compensations for high-order motion components are employed to correct the intrachannel RM and DFM and eliminate the interchannel DFS simultaneously. The effectiveness of the proposed method is verified through numerical simulations. It is noteworthy that the proposed method is capable of attaining reliable detection outcomes at high jamming-to-signal ratios (JSRs).