  In this paper we are concerned with the existence and multiplicity of
solutions for the fractional Choquard-type Schr\"{o}dinger-Kirchhoff equations
with electromagnetic fields and critical nonlinearity: \begin{eqnarray*}
\begin{cases} \varepsilon^{2s}M([u]_{s,A}^2)(-\Delta)_{A}^su + V(x)u =
(|x|^{-\alpha}*F(|u|^2))f(|u|^2)u + |u|^{2_s^\ast-2}u,\ \ \ x\in
\mathbb{R}^N,\\ u(x) \rightarrow 0,\ \ \quad \mbox{as}\ |x| \rightarrow \infty,
\end{cases} \end{eqnarray*} where $(-\Delta)_{A}^s$ is the fractional magnetic
operator with $0<s<1$, $2_s^\ast = 2N/(N-2s)$, $\alpha < \min\{N, 4s\}$, $M :
\mathbb{R}^{+}_{0}\rightarrow \mathbb{R}^{+}_0$ is a continuous function, $A:
\mathbb{R}^N \rightarrow \mathbb{R}^N$ is the magnetic potential, $F(|u|) =
\int_0^{|u|}f(t)dt$, and $\varepsilon > 0$ is a positive parameter. The
electric potential $V\in C(\mathbb{R}^N, \mathbb{R}^+_0)$ satisfies $V(x) = 0$
in some region of $\mathbb{R}^N$, which means that this is the critical
frequency case. We first prove the $(PS)_c$ condition, by using the fractional
version of the concentration compactness principle. Then, applying also the
mountain pass theorem and the genus theory, we obtain the existence and
multiplicity of semiclassical states for the above problem. The main feature of
our problems is that the Kirchhoff term $M$ can vanish at zero.
