There isn't a way to access these via the API.
It it also worth keeping in mind that the broken link reporting is only of limited use and isn't intending to be a comprehensive broken link checking solution - it only reports on broken links that Funnelback attempted to fetch during a crawl - so links that fall outside the include/exclude rules, internal links to unwanted file types (such as JS, CSS, images) and other rejected URLs (e.g. items larger than the max download size) won't be checked at all.