We propose a theory of spin relaxation of electrons and holes in two-dimensional hexagonal crystals such as atomic layers of transition-metal dichalcogenides (MoS2, WSe2, etc.). We show that, even in intrinsically defect-free crystals, their flexural deformations are able to generate spin relaxation of carriers. Based on symmetry analysis, we formulate a generic model for spin-lattice coupling between electrons and flexural deformations and use it to determine temperature- and material-dependent spin lifetimes in atomic crystals in ambient conditions.