I would recommend something like this, no need for dual chambers and using a simple blowgun. The o-ring at the breech would hold the nerf dart until enough pressure built up behind it to pop it out like a champagne cork, giving you consistent power.
The major issue is the magazine, it would have to be airtight and resistant to the firing pressure of the launcher, and making a pressure vessel with flat sides is not the best of solutions. It could be built inside a section of say 2" PVC tubing though.
Another advantage of this setup is that constant pressure on the trigger should give you full auto
If this is too radical you could go for the "conventional" option of combining a quick exhaust valve with a blowgun trigger likethis example
which would make an airtight magazine helpful but not essential.