If you can find a position with flexible hours, then I see no reason why you can't work 10-20 hours/wk while in the program. I'm in a similar position and have chosen to do some research on the side; all of my professors have suggested that it's a perfectly reasonable time commitment (as long as you don't mind sacrificing socialization, down time, etc).
I'm and ED scribe and I've loved it! It is really great clinical experience and I've learned SO much, so I would definitely recommend it. One thing you might want to look into, however, is the duration of the commitment. I know the company I work for (one of the larger scribing companies) requires a 1 year full-time commitment (4 9-12 hour shifts/week) or a 2 year part-time commitment (2 9-12 hour shifts/week). I don't know that every single company requires this, but I think that many do. If you are planning on beginning med school a year from now and can only work part time, it might not work out.
Also, the shifts can have crazy hours and (at least where I work) we are required to do night shifts. I don't really know what your class schedule/difficulty is like, but night shifts can be rough when you have class the next morning.
All that said, I still do highly recommend it if you can find a program to fit your schedule. Let me know if you have any other questions!
My schedule isn't terrible, but i do have 8 am class everyday. Hopefully I will get mostly weekends (which I know most people don't want, so that probably will be pretty easy), or the 3-11 shifts offered during the week, as opposed to the 6-2 am. My company has similar requirements, but will let you out of the 2 year part time deal if you let them know like 90 or 60 days ahead of time. It's PhysAssist/IAmScribe. Is that what you did?
They also mentioned that while they do try to schedule shifts in consideration of our class schedules, we are able to pretty easily swap or give away shifts.