The TLC chip isn't normally used for driving 7-seg displays. The chip's "special superpower" is dimming the LEDs on each of it's outputs individually and with a fine level of control. That isn't normally something you want or need to do with 7-seg displays. But there is no reason it cannot drive 7-seg displays. The displays need to be common anode. Fortunately, 5161BS is common anode.
Are you using bare tlc chips or some module with the chip soldered on? If a module, please post a link. In either case, please post a schematic diagram showing how you plan to wire everything up, and we can check it for you.