Send files via network
You may try:

Serial.println("Sending UDP message");  
Udp.beginPacket(destIp, port);
while (myFile.available()) {
  Udp.write(a);
}
Udp.endPacket();
Serial.println("Message sent!");


Or send the message part by part (for example 100bytes or 500bytes at a time)

Though, what makes you think that Arduino would be a platform that can rapidly send large files over network?
Potentially you are better off with an Raspberry Pi.