  This Letter presents the measurement of differential cross sections of
isolated prompt photons produced in association with a b-jet or a c-jet. These
final states provide sensitivity to the heavy-flavour content of the proton and
aspects related to the modelling of heavy-flavour quarks in perturbative QCD.
The measurement uses proton-proton collision data at a centre-of-mass energy of
8 TeV recorded by the ATLAS detector at the LHC in 2012 corresponding to an
integrated luminosity of up to 20.2 fb$^{-1}$. The differential cross sections
are measured for each jet flavour with respect to the transverse energy of the
leading photon in two photon pseudorapidity regions: $|\eta^\gamma|<1.37$ and
$1.56<|\eta^\gamma|<2.37$. The measurement covers photon transverse energies
$25 < E_\textrm{T}^\gamma<400$ GeV and $25 < E_\textrm{T}^\gamma<350$ GeV
respectively for the two $|\eta^\gamma|$ regions. For each jet flavour, the
ratio of the cross sections in the two $|\eta^\gamma|$ regions is also
measured. The measurement is corrected for detector effects and compared to
leading-order and next-to-leading-order perturbative QCD calculations, based on
various treatments and assumptions about the heavy-flavour content of the
proton. Overall, the predictions agree well with the measurement, but some
deviations are observed at high photon transverse energies. The total
uncertainty in the measurement ranges between 13% and 66%, while the central
$\gamma+b$ measurement exhibits the smallest uncertainty, ranging from 13% to
27%, which is comparable to the precision of the theoretical predictions.
