Flashing LED problem

What is a Gainclone amplifier?
Draw a circuit diagram of what you have and the specification of the capacitor.
Is the power switch in the mains or low voltage supply?

 

Wire the LED with a series resistor to the amp positive power rail and ground. If the switch LED has a built-in resistor to get the appropriate current from a 5V supply, approximate the forward drop of the LED based on its color, measure it's current draw from 5V, to approximate the resistor value in the switch (or if you can open the switch and measure it, do that).

Once you know that resistor value, merely subtract it from the calculated resistor value you'd need for that LED if it were powered through an external series resistor.

Perhaps it is easier to show with an equation (based on ohm's law).
5V supply
"IF" Red LED, approx forward voltage 1.8V
Measured Current (10mA = 0.01A in this example)

(5V - 1.8V) / 0.01A = 320 ohms resistor estimated to be in the switch if the above #'s are true.

Now if you had a 20V positive to ground power rail for the amp, you use the 320 ohms number above like this:

(20V - 1.8V) / 0.01A = 1820 ohms

You already have 320 ohms in series in the switch, so 1820 - 320 = 1500 ohms resistor in series from positive power rail to switch. Remember this depends on the variables above, which LED color and that forward drop voltage, and what current you measure the LED consuming off 5V.

I would also think about getting rid of the USB supply to the bluetooth module using an LM317 (configured to 5V) instead of the USB supply for powering the bluetooth module, assuming that module is a modest current consumer around 20mA or less? Cleaner power might also help it perform a little better.

I mention LM317 instead of LM7805 because it has a higher input-output voltage difference capacity. If the rail is no higher than 25V you can use LM7805 instead and not have to use a couple resistors that would've set the LM317 voltage but aren't needed for LM7805.