The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the J/ψ -> η c γ and ψ(2S) -> η c γ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative spin-flip decay widths of the 1S, 2S and 3S states of the cc, bb and B + c systems. In the B + c system the gluon exchange current also contributes to the spin-flip transition rates.