We present Anisotropic Flow Cosmology (AFC), a phenomenological framework motivated by the tension between the strict isotropy of the early universe (CMB, BBN) and the persistent dipole anisotropies observed in intermediate-redshift quasar distributions. Standard General Relativity predicts that cosmic shear decays rapidly (ρσ ∝ a −6 ), rendering the observed ∼ 1.5% Quasar Dipole (z ≈ 1.2) formally inconsistent with Big Bang Nucleosynthesis limits if extrapolated backward. We demonstrate that this paradox is resolved if cosmic anisotropy is a growing mode driven by a scalar-vector ”Dark Energy” interaction. We explicitly show that this mechanism satisfies early-universe constraints (Ωσ < 10−5 ) while reproducing late-time observational anomalies. Furthermore, we demonstrate that this specific scalar-vector coupling resolves the Belinski-Khalatnikov-Lifshitz (BKL) instability in contracting cosmologies, permitting a non-singular ”Big Swipe” bounce.