Hi @BruceWu,
The comment about symmetrization of the half-maps in 3D Flex reconstruction of TRPV1 was done via manual C4 symmetry-averaging of the half-maps (i.e. taking each half map, rotating it by 90, 180, and 270º, and adding these to the original); this was done in external software. In order to make your C3 3D Flex Reconstruction comparable to C3 non-uniform refinement, you may try something analogous in software like Chimera for example. Note we use the z-axis of the volume as the symmetry axis for Cn symmetries. You could do this averaging for each half-map and then re-import the new half-maps back into CryoSPARC and run a Validation (FSC) job.
One other option is to symmetry expand your particles via C3 symmetry before running 3D Flex Train. This will make training take longer of course, but will give the algorithm more signal to work with. The reasoning behind doing this is the same reasoning why we recommend using symmetry expansion prior to 3D Variability Analysis — you might find this previous discussion interesting. Note that even with symmetry expanded particles, the space of learned deformations and the canonical density too are not guaranteed to be C3-symmetric, for reasons discussed in the linked post.
Michael