It sounds like the power supply is failing to regulate and dropping out momentarily. The answer below seems to describe a similar scenario and the rpi wiki also mentions that the blinking PWR LED indicates an issue with the power supply.
From this question:
I have a Raspberry Pi B+ connected to an external USB disk, a Seagate
Portable 1 Tb (no external power source)
...
The red light blinking but everything working fine
The accepted answer by user @tslmy who quotes the wiki at http://elinux.org:
Red power LED is blinking
A blinking red power LED indicates problems
with the power supply. On model A and B, it is hard-wired to the 3.3V
power supply rail. If it is blinking, as one user has reported1 it
means the 5V power supply is dropping out. Use a different power
supply.
On model B+ (and presumably also the A+), the circuit has been
improved to give a much more reliable warning of poor power quality.
The red power LED is wired to an APX803 supervisor[2] which kicks in
when the 5V power supply drops below 4.63V[3]. If it does, the LED
will blink. Check your connections, cable, and power supply.
From the APX803 supervisor data-sheet:
Microprocessors (μPs) and microcontrollers (μC) have a reset input to
ensure that it starts up in a known state. The APX803/D drive the μP’s
reset input to prevent code-execution errors during power-up,
power-down, or brownout conditions. They assert a reset signal
whenever the VCC supply voltage declines below a preset threshold and
keep it asserted for a fixed period of time after VCC has risen above
the reset threshold
If the data-sheet for the model B+ is correct, the APX803 is hooked up to the red PWR LED as the wiki states. I can't account for the blinking (could it be caused by C6? Is it actually the raw input power drops you're seeing? Is it a feature of the APX803?) but it certainly shows that the APX803 can make or break the ground connection of D1 (red LED) via Q1 (depletion-mode n-channel MOSFET):
