You're correct, 'with on camera' is not a standard expression. To be 'on camera' is a normal expression, but it would not occur as 'with on camera.' It would be 'with camera on' or 'with your camera on.'
The expression 'on camera' is used as a phrase to mean 'being filmed:'
'I don't like to be on camera.'
'Everyone who walks the streets of London is on camera.'
'For the meeting, if you don't want to be on camera, you may turn your webcam off.'
'Please show up to the meeting with your camera on.'
'All students are expected to attend online lessons with cameras on.'