I don't know that you need all that - just an Arduino and a piezo speaker and a pot if you want to play with the volume.
byte speakerPin = 1;
void generateNoise() {
static unsigned long int newr;reg = 0x12345678; //seed
unsigned long int newr;
unsigned char lobit;
unsigned char b31, b29, b25, b24;
b31 = (reg & (1L << 31)) >> 31;
b29 = (reg & (1L << 29)) >> 29;
b25 = (reg & (1L << 25)) >> 25;
b24 = (reg & (1L << 24)) >> 24;
lobit = b31 ^ b29 ^ b25 ^ b24;
newr = (reg << 1) | lobit;
reg = newr;
digitalWrite (speakerPin, reg & 1);
delayMicroseconds (50); // Changing this value changes the frequency.
}