As a former Flightfox 'expert', this has changed over time. For a while, if you paid and ran a contest, and they couldn't beat your price, you could request a refund (if you proved you had a lower price), and you'd get your money back.
Then a few months back they changed their model and shut out most of the experts, changing the remainder to 'travel consultants'. The idea being instead of having a bunch of people throw prices at you, you'd get one of their best people working with you to find the lowest price.
Odds are, you're going to get amazing service. When I was competing as an expert on the site - and I consider myself reasonably good at finding flight specials, I was in awe at some of the prices some people were managing to find. I'd use the site to get other experts to beat my prices for my own travel as well. They're seriously good.
Now the terms specify:
On Flightfox, travel consultants (the "Experts") try to build you the
best trip itinerary in exchange for a fee. You pay this fee for
services rendered. If you are unhappy with the service, you may
request a refund from your expert. Your expert holds full discretion
to approve or decline refunds.
So there's no 'guarantee', and there's always a chance that you'll find the absolute cheapest fare. Nobody can promise to beat every single price. But if you're unhappy or they really can't beat you, it's in their interests to refund. In the past when I used it and they couldn't beat a YVR->SFO return flight of mine, they refunded it.
I'd probably still use them for a complex trip. They're amazing. However I now compete on darjeelin.com (see referral link in my profile if interested) as Flightfox has shut a lot of us out, which is disappointing. I've met the founders and like them and really support the site - as an 'expert' I'll use darjeelin, but as a customer, I'd still use flightfox. It's a great solution.