I need a window for imaging underwater. The water is filtered and at room temperature with a very small amount of detergent in it. It is flowing at low speed. Will a MgF2 coated window survive this for a few years?

MgF₂ has the solubility of approximately 0.0002g per 100g water at room temperature. So if the water is moving, it means that the MgF₂ will be continuously dissolving at a very slow rate. After a long period of time, the whole layer of coating may be totally removed. In addition, the detergent solution will be alkaline [depending on the detergent used, pH value will vary from 7.5 (dishwasher) to 12 (commercial grade detergent)], there is a possibility that the MgF₂ will react to form a salt which will appear as a white stain on the coating. In summary, MgF₂ would not be ideal for long term use under water. Even if you use an uncoated window, there could be some staining from the glass reacting with the detergent.