According to Kearney, distillation doesn't remove dangerous radioactive iodines (iodine is relatively volatile). He instead recommends building a clay-based earth filter, using a freshly-dug hole and taking material from more than 4" underground.
I have 2022 edition. it is conspicuously absent on distillaton.
However, distillation may or may not remove iodine which occurs in many forms but, with chlorinated water supplies, the iodine is likely to be present as iodate molecule state which isn't volatile so it will be easily removed by distillation.
