I was able to install Chekov's Lost Missions from the retail disc using the procedure below. Full post with screenshots on my blog: https://bentrubewriter.wordpress.com/2015/05/12/agfv-starfleet-academy-chekovs-lost-missions-gog
Step One: Install Starfleet Academy using the GOG installer (I haven’t tried this with Galaxy, but you may be better off with the stand-alone).
Step Two: Rename the game folder. By default the game will install to C:\GOG Games\Star Trek – Starfleet Academy. Rename this to something else like C:\GOG Games\Star Trek – Starfleet Academy GOG. Do this after you’ve installed the game, don’t change the install directory.
Step Three: Insert the Chekov CD. Don’t run the installer yet, we’ve got some files to copy.
Step Four: Copy the the “m” video folders from the movies sub-folder on the Chekov disk to the movies sub-folder in your GOG installation. These should be m03, m04, m10, m11, m24, m25 and m27. Don’t copy g00.
Step Five: In your GOG installation rename cdlist.lst to cdlist.lst.old. Rename movies.lst to movie.lst.old. Copy cdlist.lst and movies.lst from the setup folder on the Chekov disk to the movies folder in your GOG installation. You can overwrite these files, but it’s a good idea to back them up by renaming them in case something goes wrong.
Step Six: Copy the contents of the sounds sub-folder on the Chekov disk to your GOG installation’s sounds sub-folder. Again this will be m03, m04, m10, m11, m24, m25 and m27.
Step Seven: Right-click on the Chekov install executable (probably setup.exe). Click Properties, then the Compatibility tab. Run in Windows 98 / Windows Me mode, and Run as Administrator.
Step Eight: Run the Chekov install. It should detect the original installation folder, and copy the files to that location, not your renamed folder. The big thing we need is the data file.
Step Nine: Rename the Chekov folder (maybe append Chekov to the folder name), and rename the GOG installation back to the original folder name.
Step Ten: Rename data.dat in your GOG installation to data.dat.old. Copy the data.dat from the Chekov install folder into your GOG install folder. No other files should be necessary. Do not overwrite the EXE files.
Run Starfleet Academy and you should see the Chekov missions in your missions tab. These don’t intersperse with the narrative as far as I know but you should be able to play them independently. Let me know if this works for you and feel free to send any questions.