What I would do is:
1. Use seemless paper right behind the subject
2. Only use your flash as a main light. Make it come from top of camera with reflector underneath for some fill if you need it. Kind od boring but works for kids as their skin is good.
Example shot, here he is lying but you get the idea. I only used one light in a medium softbox.
Background is a wallmart blanket on his crib mattress.





