At the moment there is no way to do this automatically. However, there are some work implementing CSL in JabRef. See https://github.com/JabRef/jabref/issues/119 for the request and some further information (nothing recent though, although I believe it is an active project).
The alternative right now is to write your own jstyle file, which may appear challenging but is quite feasible if the correct formatting is know in advance. You may use https://sourceforge.net/projects/efe/ as the export filter and jstyle files are similar when it comes to entry layout. Author formatting and character formatting differs though.