As you may know, the linux_base port is designed to deliver an integrated experience with FreeBSD native programs. As such some parts of the native FreeBSD infrastructure is used. If you would try to use a Linux–compiler to generate Linux–binaries, you would run into the problem that by default the FreeBSD includes are used.
To have a fully featured and non-integrated Linux environment on your FreeBSD system either mount an existing (and compatible) Linux installation somewhere into your FreeBSD system, or install a linux_dist port. This can be done additionally to an already installed linux_base port.
When you have a complete Linux environment available, you need to mount the FreeBSD devfs to /path/to/complete_linux/dev, linprocfs to /path/to/complete_linux/proc and linsysfs to /path/to/complete_linux/sys to have a complete setup.
Now you just need to chroot into this /path/to/complete_linux and you configure/make/install or whatever you need to do to generate your desired Linux binary.