I'm using this structure:

Zombie loottable

can roll rotten flesh
can roll iron loottable

Iron loottable

can roll iron ingot
can roll iron nugget

But iron doesn't show up in EMI Loot screen.
Am I doing something wrong?

EMI Loot does display loot table entries. What type did you give the "Iron" loot table? e.g. "minecraft:chest", "minecraft:entity", etc. Or did you not give a type?

Yeah, "chest" type works fine, thanks

I would recommend using entity type if it is for an entity drop