Motivated by cold-atom experiments and a desire to understand far-from-equilibrium quantum transport, we analytically study the dynamics of spin helices in the one-dimensional XX model. We use a Jordan-Wigner transformation to map the spin chain onto a noninteracting Fermi gas with simple equations of motion. The resulting dynamics are nontrivial, however, as the spin-helix initial condition corresponds to a highly nonequilibrium distribution of the fermions. We find a separation of timescales between the in-plane and out-of-plane spin dynamics. We gain insights from analyzing the case of a uniform spin chain and from a semiclassical model. One of our key findings is that the spin correlation functions decay as t-1/2 at long time, in contrast to the experimentally observed exponential decay. © 2022 American Physical Society.