Generally, a 600 CFM rated hood or blower will move roughly 400 CFM through a reasonable duct system given sufficient make-up air. I am not aware of any hoods with two blowers, one of which is intended to be mounted on a roof. Such a configuration would be a do-it-yourself project.

A 6-inch duct is about 0.2 square feet in sectional area, so 400 CFM will cause the air velocity in the duct to be 2000 ft/min. This is the upper end of the recommended velocity range, and this itself might cause a 600 CFM rated (at zero static pressure) blower to operate at even less than 400 CFM actual. Usually one would want an eight-inch diameter duct for this purpose.

Two blowers in series can work to overcome system pressure losses, but there are potential blade to blade interactions. One might want to use different design (fan-blade-wise) blowers for such a project. Years ago I used a NuTone 600 CFM rated down-blast blower on the roof connected to a cooking center that had a propellor type fan in its hood. The difference is performance and duct-length separation eliminated potential for interaction. This was, however, and ad-hoc jury-rig type of cooking ventilation that I have now thankfully replaced with something more effective. The NuTone blower is still in service for reducing wall oven effluent at the ceiling level.

Generally, one would want to evaluate the pressure losses of the cooking hood loop and utilize a blower that moves the required air flow rate at the pressure loss associated with that flow rate.

I'm not sure your roof location would pass code in all municipalities due to the window location, and in any case, it doesn't look (from here) like it has the same exit sectional area as the already barely sufficient duct.

I recommend installing a hood that achieves the required capture and containment performance as described in myriad threads on this forum. It would not have a blower; instead, the roof blower would be used to move air down the roof, or upward, although I doubt there are many mini up-blast blowers being manufactured to achieve the latter approach.

Also, make-up air needs to be supplied to the kitchen. This is a big subject all by itself, but you can be sure that no matter how well your house is sealed so it gags the air to the hood, the hood will match it with sufficiently restricted flow.