We propose DrivingForward, a feed-forward Gaussian Splatting model that reconstructs driving scenes from flexible surround-view input. Driving scene images from vehicle-mounted cameras are typically sparse, with limited overlap, and the movement of the vehicle further complicates the acquisition of camera extrinsics. To tackle these challenges and achieve real-time reconstruction, we jointly train a pose network, a depth network, and a Gaussian network to predict the Gaussian primitives that represent the driving scenes. The pose network and depth network determine the position of the Gaussian primitives in a self-supervised manner, without using depth ground truth and camera extrinsics during training. The Gaussian network independently predicts primitive parameters from each input image, including covariance, opacity, and spherical harmonics coefficients. At the inference stage, our model can achieve feed-forward reconstruction from flexible multi-frame surround-view input. Experiments on the nuScenes dataset show that our model outperforms existing state-of-the-art feed-forward and scene-optimized reconstruction methods in terms of reconstruction.