How can I place a flower box on my window without drilling?
Are you on the first floor of your place? Given all the restrictions you have with your construction, I would say the only way you could do this is by putting your flower box on legs. You could go cheap and use patio stones for flat supports for the legs. If heavy enough, with dirt in it, the box should not move during winds. To assure it stays in place ,you might consider a strip of double faced tape along the frame you describe, or if it is empty channel, a very small clamp or two to hold the box to the frame.