  In this paper, we first establish the uniqueness and non-degeneracy of
positive solutions to the fractional Kirchhoff problem \begin{equation*}
\Big(a+b{\int_{\mathbb{R}^{N}}}|(-\Delta)^{\frac{s}{2}}u|^2dx\Big)(-\Delta)^su+mu=|u|^{p-2}u,\quad
\text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b,m>0$,
$0<\frac{N}{4}<s<1$, $2<p<2^*_s=\frac{2N}{N-2s}$ and $(-\Delta )^s$ is the
fractional Laplacian. Then, combining this non-degeneracy result and
Lyapunov-Schmidt reduction method, we derive the existence of semiclassical
solutions to the singularly perturbation problem \begin{equation*}
\Big(\varepsilon^{2s}a+\varepsilon^{4s-N}
b{\int_{\mathbb{R}^{N}}}|(-\Delta)^{\frac{s}{2}}u|^2dx\Big)(-\Delta)^su+V(x)u=|u|^{p-2}u,\quad
\text{in}\ \mathbb{R}^{N}, \end{equation*} for $\varepsilon> 0$ sufficiently
small and a potential function $V$.
