i have these 2 old Singing machine classic speakers that go to an Singing Machine Karaoke Pedestal System (https://bit.ly/2YOa9pb) that is broken I still want to use the speakers how would I power them they use a 3.5 mm headphone jack

There is no amp that will just workIf these are passive speakers (is this 3.5mm the only cable going into them?), you'll need a stereo amplifier, and cutting connectons to a bare wire.