Warning : Baked reflections will not give the result you may expect. Here is a preview of the differences. I highly recommend not doing this, but hey, it's not illegal.
Make a Material with a Texture Coordinate, Environment Texture and Emission Node. Connect Reflection to Vector, Colour to Colour then finally Emission to Surface. This will emulate reflections with an environment texture, other objects in the scene will no show. If you want other objects to show, render an equirectangular panorama at the location of the reflective object and use that as your environment texture instead. In my case, I'm going to use a HDRi image.
In the same material, create an Image Texture node and create a new image. Check 32 bit float and switch Colour Space to Filmic Log.
With the Image Texture Node and Object selected, go into the Bake settings in the Render Properties panel and change the Bake Type to Emit. Then click Bake.
Once baking has finished, you'll have an image texture to use in the material. Open the material and connect the Image Texture node to UV on a Texture Coordinate Node and Colour to Colour on an Emission node.