Chaplain can deal 4 multi hit per swing. It comes from Normal Attack, Sacrament, Last Rites, and Aspergillum. If you have Cafrisun set, it will deal another +1 additional hit, making it 5 hit per swing.
Generally Chaplain is using the “Additional Damage” mechanic to get the “multi hit” effect. In reality, it’s multiple ticks of damage. Blessing grants Additional Damage on each AA. Sacrament grants Additional Holy Damage & bonus Holy Damage to each AA. Last Rites increases Holy Property Damage in proportion to Sacrament Level. Aspergillum makes it so Aspersion Damage is applied to each AA.
So here is a example, the numbers in the example are just place holders:
So on a Single AA you get 4-ticks or hits of damage. This is further increased with Cafrisun Set which gives you Additional Earth Damage & Arde Dagger which gives you Additional Fire Damage. Note this multi-hit only applies to AAs.
To answer the second question. No, Priest is the only way for a Cleric through class abilities to get that mutli-hit effect on auto attacks.