I just started playing D&D, and I'd like to know if it is possible to add a breastplate to leather armor for an AC bonus?
Different from previous editions, armor does not give a + to AC. they set the AC to a particular value, then bonuses and penalties are applied.
Leather armor grants AC 11 (it is not a +1 to AC. It is straight 11).
Breastplate grants AC 14.
If you are a barbarian with 16 CON, you'd have AC 13 + Dex from the unarmored defense, and would not benefit from wearing leather armor.
One historical tidbit: Breastplate armor was worn over leather. It was not a hardened boiled leather cuirass like the leather armor, but a buff coat jacket.
TL;DR: Layering armor is useless for AC purposes. You would only get the biggest AC and possibly a lot of penalties.