The default behavior of a Pop-up is that when your end user performs an action on the Pop-up, the Pop-up closes. In case you have 2 buttons and each opens two different Flows, when the end user clicks any of the button the Pop-up closes. The behavior indicates that end users can only choose to play any of the Flow.
The Pop-up needs to appear again for your end users to play the other Flow attached to it. For more information, see Create Pop-ups.