Flashing LED circuit using Flyback Topology Flickering Problems
It appears CTRL2 is available to do the flashing.
Replace R22 with a transistor

Was AC power and triac dimmable a requirement?
There are easier, simpler, and much less expensive solutions to the project as posted.

By far the simplest would be to use a constant current power supply with a dimming circuit.  To flash all you would have to add would be the circuit to toggle the dimmer input with a voltage from 0V to upto 10V.  10V will set the current to the power supply max current.  Any voltage low than 10V would would limit the current to a ratio of the input to 10V.  E.g 3V would be 20% of max.

I do not believe AC should be used to power LEDs and Light Bulbs and LEDs are not a good match. Cramming LEDs in a small area is just wrong. 

I prefer a 48VDC supply, a simple LED driver circuit $3 parts cost to drive strings of 15 or 16 LEDs.