Magnetic topological insulators and semimetals are a class of crystalline solids whose properties are strongly influenced by the coupling between non-trivial electronic topology and magnetic spin configurations. Such materials can host exotic electromagnetic responses. Among these are topological insulators with certain types of antiferromagnetic order which are predicted to realize axion electrodynamics. Here we investigate the highly unusual helimagnetic phases recently reported in EuIn₂As₂, which has been identified as a candidate for an axion insulator. Using resonant elastic x-ray scattering we show that the two types of magnetic order observed in EuIn₂As₂ are spatially uniform phases with commensurate chiral magnetic structures, ruling out a possible phase-separation scenario, and we propose that entropy associated with low energy spin fluctuations plays a significant role in driving the phase transition between them. Our results establish that the magnetic order in EuIn₂As₂ satisfies the symmetry requirements for an axion insulator.