The FIFO size is fixed at 16 entries, but that doesn't mean you need to send in multiples of 16 bytes. If you're writing data to the FIFO and it's not being sent, the UART must be configured wrong. Make sure it's enabled in CFG, and check TXDIS in CTL. Verify that you have the clocking set up correctly.
I'd suggest starting with one of the MCUX SDK examples, even if you're not going to use the SDK in your project. But beware - NXP isn't very careful about testing and documenting their examples. It's common to find UART loopback examples that use a free-running oscillator as their clock source, for example. That's fine on the same board, but if you're connecting two boards their clocks might be out of spec. So while the example will almost certainly work, you should be cautious about applying it to your example.
Scott