Flexible Intelligent Metasurfaces (FIMs) enable wireless systems to adapt their three-dimensional geometry through morphing, thereby providing new spatial degrees of freedom. However, continuous deformation complicates the accurate acquisition of Channel State Information (CSI). This work proposes a multidimensional framework for MIMO systems with active FIM arrays at both the transmitter and receiver. A split single-time-scale training protocol sequentially introduces spatial variation by morphing the receiver, then the transmitter. The resulting signal model is formulated as a PARAFAC decomposition, and an alternating least squares (ALS) algorithm is employed to estimate steering matrices and path gains. Our numerical results show that the proposed channel estimation method yields accurate CSI recovery for different system setups.