Hi there, we're having the same problem.
As my designer and I noticed while building a map, you can indeed hold shift and right click to copy a tile ( or multiple tiles).
BUT it doesn't work with tiles that have been rotated / mirrored / flipped. Seems to only work with the original tiles in the Tilemap object.
It's indeed frustrating to make something that looks good and then have to make that same part over and over again
off topic: Just read through some forums and was thinking of making a post about this and today this shows up, timing ^^