Let (X,σ) be a subshift and Aut(X) be the automorphism group, the group of self conjugacies of (X,σ). The mapping class group, denoted M)(σ), is the group of self flow equivalences. We show that M(σ) is constrained in the case of low-complexity minimal subshifts, similar to constraints on Aut(X). In particular, when (X,σ) is a minimal subshift associated to a substitution, M(σ) is an extension of Z by some finite subgroup of Aut(X).