We report, for the first time, highly crystalline cyanurate-linked covalent organic frameworks synthesized via dynamic nucleophilic aromatic substitution. The high crystallinity is enabled by the bond exchange reaction (self-correction) between 2,4,6-triphenoxy-1,3,5-triazine and diphenols via reversible SNAr catalyzed by triazabicyclodecene. The CN-COFs contain flexible backbones that exhibit a unique AA'-stacking due to interlayer hydrogen bonding interactions. The isoreticular expansion study demonstrates the general applicability of this synthetic method. The resulting CN-COFs exhibited good stability, as well as high CO2/N2 selectivity.