Does similar equipment stack in Resident Evil Resistance?

Yes, equipment do stack.

I confirmed using FMJ Rounds on Becca.

Here my results after several tests on practice mode. Damage on zombies.

FMJ Rounds II : Highest weapon damage was 446 FMJ Rounds III : Highest weapon damage was 462 FMJ Rounds II & III : Highest weapon damage was 503

As you can see, same equipment stack with each other. Iron Nails should be the same but on melee damage.

I hope this helps.