One can set a password for vino through GUI or command line. An example is provided here. But is it possible to set the password of vino the same as the password for the user account automatically using the command line?
Like if the user account is ubuntu:
1) A command to read the password for ubuntu. 2) A command to write that password as the password for vino.
Well, generally no - Vino cannot use the user's account password.
As can be read in this article discussing the issues with Vino, vino does not use the standard Linux authentication mechanism called PAM (Pluggable Authentication Module).
As to your suggested mechanism - there's no way to "read the password" from the user accounting system (password database) as the value stored for the password in the password database is not the password itself but a checksum (also called a hash function result) of the actual password, so the user's password is actually not known to the system - so it cannot be stolen.
That being said, because PAM is so awesome and, well, pluggable, you can have a plugin that runs some arbitrary script - for example: to change Vino's password - whenever a user changes their password (or log in, or whatever). I've actually found such a plugin here: https://github.com/jeroennijhof/pam_script. I have not tested it so I cannot explain how to make it work, nor even I guarantee that you can use this to do what you want - but I'm sure you'd learn quite a bit while trying ;-)
