Sending data from Arduino to uVGA-II in GFX (4DGL) Mode

void setup(){

Serial3.begin(9600);
  Serial.begin(9600);

9600 baud is not going to help with the speed issues. Can't you go faster?

Your code:

int req = 5; //mic REQ line goes to pin 5 through q1 (arduino high pulls request line low)
int dat = 2; //mic Data line goes to pin 2
int clk = 3; //mic Clock line goes to pin 3
int i = 0; int j = 0; int k = 0;
byte mydata[14];
int num;


void setup(){
  Serial3.begin(9600);
  Serial.begin(9600);
  pinMode(req, OUTPUT);
  pinMode(clk, INPUT);
  pinMode(dat, INPUT);
  digitalWrite(clk, HIGH); // enable internal pull ups
  digitalWrite(dat, HIGH); // enable internal pull ups
  digitalWrite(req,LOW); // set request at LOW
  
}

void loop(){
 
// get data from mic

  digitalWrite(req, HIGH); // generate set request

    for( i = 0; i < 13; i++ ) {

      k = 0;

      for (j = 0; j < 4; j++) {

      while( digitalRead(clk) == LOW) { } // hold until clock is high

      while( digitalRead(clk) == HIGH) { } // hold until clock is low

        bitWrite(k, j, (digitalRead(dat) & 0x1)); // read data bits, and reverse order )

      }

// extract data

      mydata[i] = k;

//      sign = mydata[4]; 

//      decimal = mydata[11];

//      units = mydata[12];

    }
    
// assemble measurement from bytes    

char buf[7];

for(int lp=0;lp<6;lp++)

  buf[lp]=mydata[lp+5]+'0';

buf[6]=0;

num=atol(buf); //assembled measurement, no decimal place added

 Serial3.println(num);
 Serial.println(num);
    digitalWrite(req,LOW);

   //  delay(25); 

}

I don't see Serial3.available or Serial3.read in there. Are you trying to do you own software serial? Why?