  We study four-point functions of spinning operators in the flavor current
multiplet in four dimensional $\mathcal{N}=2$ SCFTs, using superspace
techniques. In particular we explicitly construct the differential operators
relating the different components of the super-correlator. As a byproduct of
our analysis, we report the computation of the four-point amplitudes of gluons
in bosonic Yang-Mills theories on $\mathrm{AdS}_5$ and we give evidence of an
AdS double copy relation between the gluon amplitude and its gravitational
counterpart.
