Ultrasound imaging has been developed for image-guided radiotherapy for tumor tracking, and the flexible array transducer is a promising tool for this task. It can reduce the user dependence and anatomical changes caused by the traditional ultrasound transducer. However, due to its flexible geometry, the conventional delay-and-sum (DAS) beamformer may apply incorrect time delay to the radio-frequency (RF) data and produce B-mode images with considerable defocusing and distortion. To address this problem, we propose a novel end-to-end deep learning approach that may alternate the conventional DAS beamformer when the transducer geometry is unknown. Different deep neural networks (DNNs) were designed to learn the proper time delays for each channel, and they were expected to reconstruct the undistorted high-quality B-mode images directly from RF channel data. We compared the DNN results to the standard DAS beamformed results using simulation and flexible array transducer scan data. With the proposed DNN approach, the averaged full-width-at-half-maximum (FWHM) of point scatters is 1.80 mm and 1.31 mm lower in simulation and scan results, respectively; the contrast-to-noise ratio (CNR) of the anechoic cyst in simulation and phantom scan is improved by 0.79 dB and 1.69 dB, respectively; and the aspect ratios of all the cysts are closer to 1. The evaluation results show that the proposed approach can effectively reduce the distortion and improve the lateral resolution and contrast of the reconstructed B-mode images.