@everywhere using FFTW produces "Package FFTW not found in current path"

Sorry for suggesting the obvious, but have you tried:
@everywhere Pkg.add(“FFTW”)
@everywhere Pkg.add(“SpecialFunctions”)

I just now tried and on my system, the using FFTW worked without complains. The using SpecialFunctions complained, but worked after the distributed install (I would guess you typically don’t even need a distributed install and a single local Pkg.add should work, unless your running this on some cluster setup).

Maybe a

@everywhere Pkg.status() 

will give some additional information, although it isn’t easy to decode the output due to arriving async.