TLC5940 16 PWM Output Iref Resistor
The voltage of the \$I_{ref}\$ pin is nominally 1.24V (from page 7 of the datasheet), so you can easily calculate the current for a given resistor.

The current through that resistor is not the current sunk by the chip, it is merely used as a reference to set the current drive of the output pins, where the current sunk is given as $$I_{OUT (IDEAL)} = 31.5 \frac{1.24V}{R_{IREF}}$$

As the resistor is therefore typically in the range of, say, 200Ω-10kΩ, the power dissipated is negligible.