How can I run two Skype accounts on the same Ubuntu?

Run this command on terminal:

skype --secondary

I am using Ubuntu 17.04 and have Skype beta version 5.4.0.1. and I could not run the second instance via terminal using the skype --secondary command.

The new skype application is now called skypeforlinux, therefore I used this command:

$ skypeforlinux --secondary

If skypeforlinux is not found you can try using the full path:

$ /usr/bin/skypeforlinux --secondary

If you don't see the skypeforlinux application in /usr/bin/ directory, then it is probably not installed correctly on your machine.

Hope this helps you on newer versions of Skype.

skype --help gives me this:

Usage: skype [options]
Options:
  --dbpath=<path>       Specify an alternative path to store Skype data files.
                        Default: ~/.Skype
  --resources=<path>    Specify a path where Skype can find its resource files.
                        Default: /usr/share/skype
  --disable-api         Disable Skype Public API.
  --callto <nick>
  skype:<nick>?<action>
                        These commands allow Skype links handling.
  --pipelogin           Command line login. "echo username password | skype --pipelogin"
  --version             Display version information and exit.

So you can use skype --dbpath=<path> to start another instance.

EDIT: Updated my answer according to the comment given by Pavel.