Manually operated Gatling guns are fine.
ATF and its predecessor agency, the Internal Revenue Service (IRS), have historically held that the original, crank-operated Gatling Gun, and replicas thereof, are not automatic firearms or machineguns as defined. See Rev. Rul. 55-528, 1955-2 C.B. 482. The original Gatling Gun is a rapid-firing, hand-operated weapon. The rate of fire is regulated by the rapidity of the hand cranking movement, manually controlled by the operator. It is not a "machinegun" as that term is defined in 26 U.S.C. 5845(b) because it is not a weapon that fires automatically.
Electronically operated is different. The BATFE is flexible with trigger definitions. Look up the Stutter Gun, for example. Anyways, for something like this, the argument is that the "go" button is now the trigger, and one push of it allows for automatic fire.