All soluble inorganic iodides can be easily converted to iodine by oxidation in acidic, basic or neutral media.
Reaction with H2O2, even diluted, goes immediately.
2KI + H2O2 = 2KOH + I2.
It is better to acidify reaction because KOH can react further with iodine., eg:
2KOH + I2 = KOI + KI + H2O