We study the Feynman graph structure and compute certain exact four-point correlation functions in chiral CFT$_{4}$ proposed by Ö. Gürdŏgan and one of the authors as a double scaling limit of γ-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 thecorresponding 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.