SPI Daisy chained shift register

See 9.4:
In the Normal Mode phase, the serial data can be transferred into TLC591x through the pin SDI, shifted in the
shift register, and transferred out via the pin SDO. LE(ED1) can latch the serial data in the shift register to the
output latch. OE(ED2) enables the output drivers to sink current.

So you send out 8 bytes using SPI.transfer() and then toggle the LE pin High and back low to latch the data into the output registers.
You can have multiple unique LE pins, one for each device, and don't daisychain the data signal (MOSI) from device to device.
Or connect them per Figure 20, with daisychained data line, and send out 8 bytes * # of chips you have, latching them into the output stage with a common LE pin.

CrossRoads:
See 9.4:
In the Normal Mode phase, the serial data can be transferred into TLC591x through the pin SDI, shifted in the
shift register, and transferred out via the pin SDO. LE(ED1) can latch the serial data in the shift register to the
output latch. OE(ED2) enables the output drivers to sink current.

So you send out 8 bytes using SPI.transfer() and then toggle the LE pin High and back low to latch the data into the output registers.
You can have multiple unique LE pins, one for each device, and don't daisychain the data signal (MOSI) from device to device.
Or connect them per Figure 20, with daisychained data line, and send out 8 bytes * # of chips you have, latching them into the output stage with a common LE pin.

Aha that did the trick! Thank you! I have read that datasheet many times, but I can only understand so much of it.

 SPI.transfer(shiftregister);
  digitalWrite(latchpin,HIGH); 
  digitalWrite(latchpin,LOW);

Now I also understand the schematic better on page 17 (I attached). There you can also see that they put the latch high and low after they transferred the data.

The daisy chaining also works like a charm.

Thank you all for the help!