We study afterglow flares of gamma-ray bursts (GRBs) in the framework of the late internal shock (LIS) model based on a careful description for the dynamics of a pair of shocks generated by a collision between two homogeneous shells,. First, by confronting the model with some fundamental observational features of X-ray flares, we find some constraints on the properties of the pre-collision shells that are directly determined by the central engine of GRBs. Second, high energy emission associated with X-ray flares, which arises from synchrotron self-Compton (SSC) emission of LISs, is investigated in a wide parameter space. The predicted flux of high energy flares may reach as high as $∼ 10^{-8}\rm erg cm^{-2}s^{-1}$, which is likely to be detectable with the Large Area Telescope (LAT) aboard \textit{the Fermi Space Telescope} ; Comment: 18 pages, 7 figures, accepted for publication in ApJ