Upvote:2
Brussels and Geneva are both in the Schengen area. For this reason, the flight to Geneva will depart from another part of the airport than the flight from Ouagadougou and there will generally be no passport check on arrival in Geneva.
Because of that, an airport transit visa is not enough and the US green card does not help either. You will enter the Schengen area in Brussels and leave it in Geneva, with a passport check and stamp in each case and for that you need a regular Schengen visa (if you are a citizen of Burkina Faso).
See also Do I need a visa to transit (or layover) in the Schengen area?