Multi-center clinical trials utilizing quantitative diffusion kurtosis imaging (DKI) protocols require accurate, precise, and stable phantoms for validation of derived imaging metrics. This study examines the precision and reproducibility of isotropic (i)DKI parameters obtained from a phantom based on nanostructured vesicles that restrict diffusion and mimic tissue cellularity. Ten test-retest iDKI studies were performed on four scanners at three imaging centers over a six-month period. The tested prototype phantoms exhibited physiologically-relevant and highly-repeatable apparent diffusion and kurtosis parameters. Achieved precision was sufficient to characterize thermal and temporal stability trends to guide robust quantitative iDKI phantom production.