In 1973, B. Y. Chen and K. Yano introduced the special conformally flat space for the generalization of a subprojective space. The typical example is a canal hypersurface of a Euclidean space. In this paper, we study the conditions for the base space B to be special conformally flat in the conharmonically flat warped product space $B^n{ imes}_fR^1$. Moreover, we study the special conformally flat warped product space $B^n{ imes}_fF^p$ and characterize the geometric structure of $B^n{ imes}_fF^p$.