From what I understand you can’t earn while claiming MA. You’re allowed a few “keeping in touch days” but not to work regularly. Which is rubbish!
You can take on work for up to 10 KIT days without affecting your MA payment. You do have to keep a record of the days worked or DWP will make their own estimates. Anything more than 10 days disqualifies you. What you might have been seeing online is that you can take on self employed work while receiving SMP but that doesn't apply in this case.
I’m in the same boat so would be interested to see if anyone has any info 😊