Magnetic Resonance Spectroscopic Imaging (MRSI) is an essential tool for quantifying metabolites in the body, but the low spatial resolution limits its clinical applications. Deep learning-based super-resolution methods provided promising results for improving the spatial resolution of MRSI, but the super-resolved images are often blurry compared to the experimentally-acquired high-resolution images. Attempts have been made with the generative adversarial networks to improve the image visual quality. In this work, we consider another type of generative model, the flow-based model, of which the training is more stable and interpretable compared to the adversarial networks. Specifically, we propose a flow-based enhancer network to improve the visual quality of super-resolution MRSI. Different from previous flow-based models, our enhancer network incorporates anatomical information from additional image modalities (MRI) and uses a learnable base distribution. In addition, we impose a guide loss and a data-consistency loss to encourage the network to generate images with high visual quality while maintaining high fidelity. Experiments on a 1H-MRSI dataset acquired from 25 high-grade glioma patients indicate that our enhancer network outperforms the adversarial networks and the baseline flow-based methods. Our method also allows visual quality adjustment and uncertainty estimation.