Rust is probably the most trendy language offering linear types at the moment, although I'd say it much closer to being "a safer C" than "a linear OCaml", so it wouldn't really make things more functional (although it would be safer!).
ATS is descended from DependentML, but for some reason most ATS code I've seen is written in a "safer C" style too. Maybe that's just pragmatism, since ATS has very few native libraries, so it's usually easier to call out to C.
Linear Lisp might be a nice choice, but its dynamic typing may be a problem for security-critical code.