Why are silver halides insoluble in nitric acid
Nitric acid (even concentrated) is essentially an aqeuous solution.

Effectively, silver halides will not dissolve in water (they  have incredibly low $K_\text{sp}$), so the reaction indicated is moot.... there is no appreciable concentration of bromide in solution to be oxidized.

$K_\text{sp}(\ce{AgBr}) = 5.0\times10^{-13} \Rightarrow [\ce{Br-}] \approx 700~\text{nM}$