Q:

How do the Flames work?

I'm a little unclear on the wording of the Flames. What does "Empty" mean? Does it ignore mountains? Shields? I'm fairly certain it ignores troops.
Side question (maybe this should be a separate question?!) can Flames travel through the Great Brass Pipe?

A:

Empty does not mean "needs 2 critters to conquer" it means without monster or race tokens.
From the rules, bottom of page 9

A Region is deemed non-empty if, and only if, it contains at
  least one Monster or Race token (Active or In Decline). A Region
  that contains a Black Mountain marker, a Popular Place or a
  Righteous Relic but no Monster or enemy Race token is
  considered empty.

The Great Brass Pipe considers spaces adjacent for the purposes of the owning race, so Flames should be continuous through it.  This is confirmed in the FAQ.

