My purpose is a flatten tif which looks exactly the same as the original (e.g. opened in Photoshop). Layers should be merged and transparency retained.
First off, PS uses background transparency and alpha transparency (two kinds). IM only has alpha transparency. So PS background transparency is converted to alpha transparency in IM.
There is no way that I know to flatten the tiff image in IM so that you convert the alpha transparency to background transparency or make some color into transparent so as to remove the alpha channel and save as tiff.
Your image only has one RGBA frame/layer. And your alpha channel is nearly binary with a little anti-aliasing at the edges. So try
convert ImageWithTransparency.tiff -background black -flatten result
This will make your image look correct where not fully transparent and the rest will be black.
If you want to use another background color then use -background somecolor. The default is white, I believe. If you use -background none, you will not be removing the alpha channel. The image will retain its transparency and be identical to your original
There is no way to "merge" the alpha channel with the image without using/picking a background color. Alternately, you can make a checkerboard image of the same size and flatten your image onto the checkerboard so that it looks similar to what you see in PS with background transparency.
If I misunderstand what you mean by merging, please clarify.