24bit SPI word size for AD5686 Chip

Read this:

Take a clooser look at first picture and look to the SS line.It stays low during 3 bytes transfer like you want.
The reason for that is in the code Nick provide above:

// Written by Nick Gammon
// January 2011

#include <SPI.h>
#include "pins_arduino.h"

void setup (void)
{
}


void loop (void)
{

  
  digitalWrite(SS, HIGH);  // ensure SS stays high

  // Put SCK, MOSI, SS pins into output mode
  // also put SCK, MOSI into LOW state, and SS into HIGH state.
  // Then put SPI hardware into Master mode and turn SPI on
  SPI.begin ();

  delay (5000);  // 5 seconds delay to start logic analyser.

  char c;
  
  // enable Slave Select
  digitalWrite(SS, LOW);    // SS is pin 10
  
  // send test string
  for (const char * p = "Fab" ; c = *p; p++)
    SPI.transfer (c);

 // disable Slave Select
 digitalWrite(SS, HIGH);

 // turn SPI hardware off
 SPI.end ();
 
 while (1);  //loop
}

Your answer and solution is just puting down the SS line using digitalWrite(SS,LOW),then transfer all 3 bytes using SPI.transfer() and then pull the SS line up using the digitalWrite(SS,HIGH).
This will insure your SS line will be low during the 3 bytes transmission to the DAC.
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