This is Semmle's business model (https://semmle.com/). They have a custom Datalog with OO features they call QL.
I've heard LogicBlox used to do program analysis as well, but AIUI they turned more towards business analytics and then got bought out, and the Datalog engine team all jumped ship.
The Rust compiler has been exploring implementing some of their type system (the borrow checker, I think?) in a Datalog.
On the academic front, Tamás Szabó and Sebastian Erdweg have been working on an incremental Datalog engine for static analysis; https://github.com/szabta89/IncA. I know Tamas has worked for Itemis, but I don't know whether they're using this tech.
I'm working on a functional language, Datafun, inspired by Datalog, but it's too much of a toy to do any real analysis with at the moment. All in all, Datalog is still a niche language and static analysis a niche application of it, but it seems to be on the rise.