Ultrasonography offers an inexpensive, widely-accessible and compact medical imaging solution. However, compared to other imaging modalities such as CT and MRI, ultrasound images notoriously suffer from strong speckle noise, which originates from the random interference of sub-wavelength scattering. This deteriorates ultrasound image quality and makes interpretation challenging. We here propose a new unsupervised ultrasound speckle reduction and image denoising method based on maximum-a-posteriori estimation with deep generative priors that are learned from high-quality MRI images. To model the generative tissue reflectivity prior, we exploit normalizing flows, which in recent years have shown to be very powerful in modeling signal priors across a variety of applications. To facilitate generaliation, we factorize the prior and train our flow model on patches from the NYU fastMRI (fully-sampled) dataset. This prior is then used for inference in an iterative denoising scheme. We first validate the utility of our learned priors on noisy MRI data (no prior domain shift), and then turn to evaluating performance on both simulated and in-vivo ultrasound images from the PICMUS and CUBDL datasets. The results show that the method outperforms other (unsupervised) ultrasound denoising methods (NLM and OBNLM) both quantitatively and qualitatively.