Insulating under a bay window
It looks like there is a layer of foam between the siding and the house this was quite common. 
I would not seal below the siding, this could trap moisture and since there is a layer of foam attached to the sheeting there really shouldn’t be any air movement and this is outside the structure, the stud bays them selves are another air space beyond that.

I might consider adding some insulation in the air chase and use spray foam to seal it in place , remember whatever you add for insulation will limit your flow but I can’t believe you need 2 bays for flow and if one is a supply and one is a return,,, well I hope their is some kind of duct work we cannot see to rout them away from each other. 
The reason I would not seal the bottom is it can trap moisture, most of the siding I installed had weep holes as it did condense moisture into water at times.