It looks like the reaction $\gamma \to 2\gamma$ is not dynamically but kinematically forbidden.

As Dexter Kim points out, the only way to conserve energy and momentum is that the two photons are emitted at $0°$, in which case the angular momentum along the direction of motion is given by the coupling of the two photon spins.

We must remember that the photon's spin can assume only the values $m=\pm 1$. Looking at the $1+1\to 1$ Clebsch Gordan table, we then realize that the only possible coupling of two photon's spins with $j=1$ has $m=0$. But, again, the initial photon has $m=\pm 1$. Therefore, angular momentum cannot be conserved together with energy in $\gamma \to 2 \gamma$.

It looks like the reaction $\gamma \to 2\gamma$ is not only dynamically forbidden (Furry's theorem), but also kinematically forbidden.

As Dexter Kim points out, the only way to conserve energy and momentum is that the two photons are emitted at $0°$, in which case the angular momentum along the direction of motion is given by the coupling of the two photon spins.

The photon's spin can assume only the values $m=\pm 1$. Looking at the $1+1\to 1$ Clebsch Gordan table, we realize that the only possible coupling of two photon's spins with $j=1$ has $m=0$. But, again, the initial photon has $m=\pm 1$. Therefore, angular momentum cannot be conserved together with four-momentum in $\gamma \to 2 \gamma$.