LED matrix and current sink

Hi everyone, I'm trying to implement the circuit shown in the schematic below (not complete, just for reference), where the idea is to turn on only one LED at a time -hence the ADG1406- with a frequency of about 1kHz.

The characteristic of the circuit, which I try to make evident with the color gradient, is the high resistance of the traces, where green is a low resistance (15Ω) and red high (250Ω). It is because of that, I decided to implement a current sink (TLC5947) to keep the brightness constant along the whole matrix.

Using the TLV61048 (boost converter) a voltage of 14V is defined with a maximum current of 300mA, for my application, the LEDs require a current of 10mA.

Schematic

Now, my question is.

With the implementation of the TLC5947 the supplied voltage (14V) is going to be adapted according to the conditions of each led plus keeping the current constant? following more or less this equation

V=R×ILED+VLED

or in the case of implementing a current sink, the voltage supply must be different?
There must be a working principle/theory that I'm not getting.

Thanks

EDIT:
I just want to point out that I'm aware that the current set resistor (R_{IREF}) is missing, the main point of the question is to clarify the behavior of the voltage across the matrix given a current sink.
Also, the high trace resistance is given by the really small cross-section of the copper.

EDIT2:
TLC5947 dimming function its unecessary for my application. an alternative might be the TLC5923

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