You could do it with discrete logic, namely:
A pair of 555 timers, on for the 3 Hz blinking, the other for the 1 second delay
A counter, possibly a 4017, to count three flashes and reset.
A flip-flop, to steer the flash sequence between wings and tail.
and several gates to perform the glue logic for all of the above.
We are talking 5 or 6 IC packages, perhaps.
However......How proficient are you with microcontrollers?
With a microcontroller, the code for the flash sequence should be a piece of cake.