The sentence in question:
借金が雪だるま式に増えてってるって噂だよ
My best guess is that the first って is a contracted from of いる. Whatever it is that we're addressing seems to be suffering from a financial crisis. Then why not put it like 「増えているって噂だよ」, rather than what it is?
This 増えてってる is a contraction of 増えていってる (or 増えていっている).
Here いって(い)る is the progressive of the subsidiary verb いく. (This verb derives from 行く, but being a subsidiary verb is usually written in kana.)
Attaching to a main verb (here 増える) it characterizes the action described by this verb as ongoing or as getting stronger.
借金が雪だるま式に増えてってるって噂だよ
people say that debt keeps on multiplying like a snowball effect, but that's not true
For more general information about subsidiary verbs see What is a subsidiary verb?
