I have the same issue. Found this workaround:
1: Stop all running skype instances.
2: Copy the directory where skype stores its options: [in home directory] cp -a .Skype .Skype2
3: Start one instance as usual
4: Start the second with skype --dbpath=~./.Skype2
Hope that helps...
I tried exactly as you suggested and that's what didn't work...
What *DID* work was when I started all three accounts in one command with & between each one.
eg: skype --dbpath=~/.Skype1 & skype --dbpath=~/.Skype2 & skype --dbpath=~/.Skype3
Hope this helps someone else.
You can use the same solution as for MacOS. For linux it will be:
sudo su -c "nohup skype && exit" (type this in terminal)
The advantage is that when you close terminal window the skype still working