Okay, so let's just say that since the Greens' plan is going to be taking place in the middle of a populated area, it wouldn't be unreasonable for there to be innocent bystanders caught up in all the chaos. And let's also say that maybe, just maybe, Mikami's neighbor (who is watching his son for him today) decided that it was a nice enough day to go out and get some fresh air. And they happen to be in the same area as the traffic accidents and explosions that the Greens are behind. So they get separated during all the chaos and somehow (I'm not sure about this part yet. Maybe one of the reds or greens is feeling sympathetic for the small kid who's clearly injured, he could be unconscious or something along those lines, and alone during everything that's going on that. So they take him back to their base) either JUNGLE or HOMRA ends up with the Blue King's son in their possession without knowing about it. 

I was also considering throwing in the idea of him being some kind of strain. Maybe one who's powers focus around healing (ie, he himself heals at a faster rate that normal people, he can heal others at the expense of his own energy. He can accelerate healing processes by imposing other people's injuries on himself so that he's the one hurt now and can do the opposite of imposing his own injuries on others). But that might be too much.