No bonus XP from heirlooms

Dragonflight

The experience bonus has been replaced with a new set bonus feature to help your character throughout the leveling experience.

The new set bonus can be unlocked from all Heirloom pieces except weapons and trinkets. To activate the set bonus, the equipped item must be higher level than the character equipping it. For example, equipping a level 34 item on a level 39 character will not unlock a set bonus.

More information about this patch change can be found here. 

Wrath of the Lich King Classic

Heirloom items in Classic increase the amount of experience received. For more information, you can check this Wowhead guide.