Constant-current driving with LED Driver and Boost DC/DC converter
from what I know, I should drive LEDs by constant current, not
  constant voltage


Isn't that why you chose the TLC6C5912 LED driver: -



So, choose a voltage boost converter to give you circa 30 volts and you should be good to go. The one you indicated in your question (TPS61096A) might do but, bear in mind that it runs from a 5 volt rail normally and, has output current restrictions that may reduce the amount of current you might want to deliver to your LEDs.