I have a feeling they won't stack due to both using percentages, but there is no info on the Internet I can find.
They do stack. Absent any rule that says otherwise (and Pathfinder is absent of rules that say otherwise), the math works exactly like normal math: Ant Hauls' 3× carrying capacity and Burdenless armor's 50% increase (which is the same as 1.5×) just straight multiply together to give 4.5× carrying capacity.
The only alteration of multiplication rules in Pathfinder is for modifiers to rolls, which use special rules (PFRPG Core Rulebook, p. 12) to keep roll modifiers from being multiplied into the stratosphere. Carrying capacity isn't a roll bonus or penalty, so multipliers to it behave as-written, in normal mathy ways.