ideally i want to connect my karaoke machine to my tv and have the sound come out of the sonos beam

I assume your Beam is connected to the tv and you’ve set the tv to use external speakers - ie the Beam? What output does the karaoke device have? Connect it to the appropriate tv input port - HDMI or whatever. Select that input on your tv. Music will come out of the Beam. 
 

However… 
 

There may be a slight delay, which may prove distracting as your singing may seem to be a little ahead of what you’re hearing.