We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_4$ proposed by {O}.G{u}rdou{g}an and one of the authors as a double scaling limit of $gamma$-deformed $mathcal{N}=4$ SYM theory. We give full description of bulk behavior of large Feynman graphs: it shows a generalized dynamical fishnet structure, with a dynamical exchange of bosonic and Yukawa couplings. We compute certain four-point correlators in the full chiral CFT$_4$, generalizing recent results for a particular one-coupling version of this theory -- the bi-scalar fishnet CFT. We sum up exactly the corresponding Feynman diagrams, including both bosonic and fermionic loops, by Bethe-Salpeter method. This provides explicit OPE data for various twist-2 operators with spin, showing a rich analytic structure, both in coordinate and coupling spaces.
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