I'm sorry but you can't possibly be serious. There is no sane motivation for a *FactoryFactoryFactory class. No problem on earth is complex enough to benefit from that much abstraction.
What, serious about wanting to know why it is in their codebase? Yes, I'm 100% serious. If they're currently using it in production I'd assume there's a good reason for it. Plus, I'm pretty sure the folks over at LinkedIn engineering are definitely serious. In any case I'm very curious as to why (rightly or wrongly) it's in there.
It's in their codebase because they catastrophically over engineered it. Even the largest codebases on earth don't require FactoryFactoryFactory's.