  We reanalyze the $B\to M$ tensor form factors in a covariant light-front
quark model, where $M$ represents a vector meson $V$, an axial-vector meson
$A$, or a tensor meson $T$. The treatment of masses and mixing angles in the
$K_{1A,1B}$ systems is improved, where $K_{1A}$ and $K_{1B}$ are the $^3P_1$
and $^1P_1$ states of the axial-vector meson $K_1$, respectively. Rates of
$B\to M\gamma$ decays are then calculated using the QCD factorization approach.
The updated $B\to K^*\gamma$, $B\to K_1(1270)\gamma$, $K_1(1400)\gamma$ and
$K_2\gamma$ rates agree with the data. The $K_1(1270)$--$K_1(1400)$ mixing
angle is found to be about $51^\circ$. The sign of the mixing angle is fixed by
the observed relative strength of $B\to K_1(1270)\gamma$ and $K_1(1400)\gamma$.
The formalism is then applied to $B_s\to M$ tensor form factors. We find that
the calculated $B_s\to \phi\gamma$ rate is consistent with experiment, though
in the lower end of the data. The branching fractions of $B_s\to
f_1(1420)\gamma$ and $f'_2(1525)\gamma$ are predicted to be of order $10^{-5}$
and it will be interesting to search for these modes. Rates on $B_s\to
f_1(1285)\gamma$, $h_1(1380)\gamma$, $h_1(1170)\gamma$, $f_2(1270)\gamma$
decays are also predicted.
