You can use your menu launcher creator (or right click the desktop and select new launcher, depending on what desktop you are on) to fashion two new firefox launchers. The command you need for each launcher is, for example:

firefox -Profile /home/mike/.mozilla/firefox/55divdmr.Mike2 -no-remote

This will launch firefox with that profile and make sure that it doesn't connect to any other running instance of firefox with the essential -no-remote switch.

If you wanted to do it manually, the desktop shortcut would look something like this; you could create it in a text-editor and name it firefox2.desktop:

[Desktop Entry]
Type=Application
Name=fox2
Comment=my second profile
Exec=firefox -Profile /home/mike/.mozilla/firefox/55divdmr.Mike2 -no-remote
Path=/home/mike
Icon=/my/icon/location
Terminal=false
StartupNotify=false

Something else I recommend is going to your firefox folder ( mine is /home/mike/.mozilla/firefox) and checking that the StartWithLastProfile setting in profiles.ini is false:

[General]
StartWithLastProfile=0

This is because it can get confusing if you are using different profiles and you start firefox as normal without using a special shortcut and it just loads the last profile used.

You can also get prompted each time for which profile to use by making sure 'don't ask at startup' is unchecked, which is in the firefox ProfileManager settings below. This setting is reached with

firefox -ProfileManager -no-remote

as noted in the question you referred to.

For more information on the command switches available for firefox see man firefox or the Ubuntu manpages online. Further support is available at mozilla.org.

How to set up different Firefox profiles for the same Ubuntu user and the same Firefox installation

Excerpt of the command-line options from man firefox:

-ProfileManager
   Start the profilemanager. Use this to choose the profile you would like to
   run firefox with. You will need to also use -no-remote if there is already
   a running firefox instance.

-P profile
   Start firefox with the profile named profile. Will start the profile
   manager if a valid profile name is not specified. You will need to also
   use -no-remote if there is already a running firefox instance.

So you just need to start Firefox with one of those parameters by either using a terminal, the Alt+F2 HUD, from the launcher icon's context menu after editing its configuration file, which I will describe below.

Set up a new profile:

• Launch Firefox's ProfileManager from the terminal or with Alt+F2:

  firefox -ProfileManager
  

  

• Rename your current profile default to profile1 (or whatever you like, you don't even have to rename it, but I will do in this guide for clarification - you just have to replace profile1 with your exact name wherever it occurs!) by clicking on Rename Profile....

• Create a new profile with the wizard by clicking on Create Profile.... It will show you an info window first, read it and click Next. The second window will ask you to enter a name for the profile, enter profile2 here (or replace it wherever it occurs in this guide with exactly what you entered instead). I would recommend you not to change the folder where the profile will be stored in, unless you have a good reason to do so. Click Finish.

  

• Exit the ProfileManager.

Set up your launcher icon to access those profiles from the context menu:

• Copy the original launcher file (which is owned by root, used system-wide and will get replaced with the next update) to your home folder:

  cp /usr/share/applications/firefox.desktop ~/.local/share/applications/firefox.desktop
  

• Edit the copy e.g. with either Gedit (GUI) or Nano (terminal):

  gedit ~/.local/share/applications/firefox.desktop
  nano ~/.local/share/applications/firefox.desktop
  

• Search for the line:

  Actions=NewWindow;NewPrivateWindow;
  

  and add new context menu action identifiers like this (example names, but only used within the file, you won't see them anywhere else):

  Actions=NewWindow;NewPrivateWindow;Profile1;Profile2;ProfileManager;
  

• Insert the code snippet below at the end of the file, you may vary the Name= value and add as many translations as you want (example for German [de] is given). The Exec=firefox -P ... lines have to contain the exact (case-sensitive) name of the profiles you created in the profile manager! The -no-remote flag allows multiple firefox profiles to run at the same time. Also the last word in the lines [Desktop Action ...] has to exactly match the keys you added to the Actions= line above.

  [Desktop Action Profile1]
  Name=Run Firefox with profile 1
  Name[de]=Firefox mit Profil 1 starten
  Exec=firefox -P profile1 -no-remote
  OnlyShowIn=Unity;
  
  [Desktop Action Profile2]
  Name=Run Firefox with profile 2
  Name[de]=Firefox mit Profil 2 starten
  Exec=firefox -P profile2 -no-remote
  OnlyShowIn=Unity;
  
  [Desktop Action ProfileManager]
  Name=Open Firefox profile manager
  Name[de]=Firefox Profilmanager öffnen
  Exec=firefox -ProfileManager -no-remote
  OnlyShowIn=Unity;
  

• Now if you want to specify a permanent default profile for when you left-click the launcher icon (otherwise the profile you last used through the ProfileManager with the respective checkbox ticked gets launched), you also have to edit the main Exec= line. It's the topmost and should look like this:

  Exec=firefox %u
  

  Edit it to look like the one below, maybe replacing profile1 with the correct default profile name you wish.

  Exec=firefox -P profile1 %u
  

• You have to reboot (maybe logging out and back in is also enough?) before the system realizes that you want to override the system-wide firefox.desktop file and use your personal and customized one. Or you can use the command

  desktop-file-install --dir=~/.local/share/applications ~/.local/share/applications/firefox.desktop
  

  to re-initiate the launcher file. After that, enjoy your multiple profiles!