I hadn't noticed before that the Heirloom chest has the same experience bonus/boost as the Heirloom shoulders. Does the boost in experience from the two items stack? And is it additive or multiplicative? I.e. Do you get +20% more exp?
Indeed the bonus from the Shoulders and the Chest heirlooms has been designed to stack. I believe the stack is multiplicative (1.1 x 1.1) but I'm unsure on this regard. You'll get no worse than a 20% XP bonus, however. Note: as of Patch 3.2.2 these also work in battlegrounds, and with BG's being a great place to level at a high enough level, this is very good news indeed!
Indeed, equipping shoulders +10% and chest +10% will give you the cumulative 20% extra XP gain. To really speed things up, I definitely recommend a weapon, particularly for melee classes as it also scales with every level and will always give you the best gear/stat allotments for your current level.
Yes. The bonus stacks. Blue post. As to Additive versus Multiplicative: I /believe/ the bonus is additive, but I'm not certain on that, and can't find conclusive information at the moment. It's a 1% difference in XP gain, so it's not a big deal either way.
Please do note that Blizzard has announced that these items will not work past level 80, so don't think about stockpiling them for the expansion.
Another point to add is that heirloom items were not supplementing xp in BGs prior to 3.2.2 so if you did not enjoy the gains in xp prior to the patch they may be more attractive now. The bonus do not multiple. They stack 20 plus 20 [can't figure out how to do symbols on my phone lol].
It's additive gains - you will receive 1.2x XP gain for mob kills and quest turn-in with shoulders and chest. It also stacks with rested XP -- but rested doubles this gain, so this time it's multiplicative, not additive -- giving us 100 XP% + (10% + 10%) * 2 = 2.4x XP gain. Remember that quest turn in and exploration XP does not subtract from your rested total, however all gains from mob kills will, so you will burn through rested XP faster with heirloom items.
Furthermore, these stack with triple xp bonuses you may get when you use the recruit a friend system.
But triple xp stops at 60. The heirloom items stop at 80.
Lots of good answers here - here's my added 2c:
It should be noted that Honor Weekend BGs do not add any extra experience gained via Battlegrounds.
So stick to the Battleground of your liking/AV for maximum enjoyment/leveling.