It should be possible to apply the use function to any object which implements the AutoCloseable interface.
java.sql.Connection is a sub-interface of AutoCloseable and so I’m surprised that it doesn’t compile.
But, if it doesn’t, then your try/finally close() approach is fine as use is basically a wrapper for that when using AutoCloseables and similar to Java’s try-with-resources statement.
AutoCloseable was introduced in JDK 7. You should add dependency on, at least, kotlin-stdlib-jre7 (you can also have kotlin-stdlib-jre8 instead) to your project to be able to use use with AutoCloseable classes like JDBC Connection.