When attempting to use either the NBT tag ArmorItems or HandItems, the mob you are summoning will not have the item. I have used the command /summon minecraft:zombie ~0 ~1 ~0 {HandItems:[{id:diamond_sword},{}]} and /summon minecraft:zombie ~0 ~1 ~0 {ArmorItems:[{},{},{},{id:chainmail_helmet}]}.
Dupe of MC-105968