I am trying to design a VTOL system for a drone and I don't want to have extending motor arms that make it look like a quadcopter. I want to use duct fans and thrust vectoring nozzles. However, the aircraft is 25 kg and the drag caused by vertical takeoff is 2 N. But most of the RC duct fans I see online can only deliver 2 to 3 kg of thrust. So I am thinking whether I can put two ducted fans behind one another, but how much more thrust can I get? will it be the sum of the two motor, or other numbers?
No, two fans stacked in series will not produce the same static lifting force as two fans in parallel. Several factors will be in play.
First is that by default the ducted fan blade angles will be assuming intake air at low speed. If you want to add a second stage it needs to have an a higher angle of attack on the second stage (something like the changing slope of a single fan blade but stretched across two fans). This can be partially achieved by increasing RPM but that moves away from the optimal power point of the motors unless major re-design is done.
The second is that the cross sectional area needs to change. If you have one fan capable of pulling 1 cubic meter if air through it's intake per second and pushing it out at 1 meter per second, it is moving one cubic meter per second. If the following stage is increasing that to 2 meters per second, it is trying to pull 2 cubic meters per second from the first stage! Hence the taper seen in multi stage turbines.
The third is drag through the combined duct. Drag goes up with square of speed, so the details of the surface finish and motor supports starts to matter far more than the original designer intended, so for example helicopter design.
Blades also work best in undisturbed air, and the airflow going into stage two or three of a stack will not be that without carefully designed stators between stages.