question

I'm not seeing anything suggesting that server allows external queries, the only thing I found was documentation for hosting your own brouter server.
Perhaps I'm just not looking in the right place though.

The project behind it appears to be this : abrensch/brouter: configurable OSM offline router with elevation awareness, Java + Android (github.com)

And it does mention an HTTP server you can run, which I'm guessing is what you're looking for, it also links to the source file which documents the server API (server endpoints), you'd need to emit requests from FlexSim which this specific server understands, and translate its responses back to what FlexSim expects.

I'm assuming this is the sea route server question you're referring to : How to connect GIS to a SeaRoute server? - FlexSim Community
You will need to follow the same process here as is described in that answer : extend the GIS navigator to format requests in the way your server expects to receive them, and interpret its responses.

Perhaps someone has done this before and will be able to give you a working example, but if not, maybe these pointers can get you going in the right direction.