Hidden Mac Dock Icon

This solution worked for me, but it might depend on the application in question. I tried it with a 3rd party app called "Burn" and it worked.

    Go to your applications folder and right click (control-click) on the app you wanna hide from the dock.

    Click on Show contents. You should now be able to see "inside" the app's files.

    Open the Info.plist file in the Contents folder with TextEdit (right click -> "Open with...")

    Go to the very bottom of the file and find the last two lines which should say:

        </dict>
        </plist>

    Now insert this before these two lines and save the file.

        <key>LSUIElement</key>
        <true/>

After this the app's dock icon will not be shown anymore. Keep in mind that you will need to use the Activity Monitor or Terminal (killall <appname>) to quit the app if you close the window.

If closing the window quits the app, you can press cmd + h to hide the window. This should make your app completely invisible.

To make it visible again, just remove those two lines again and the app should behave like before.