Well it looks like their flasher is integrated into the bulb itself.
If you would still like to use original bulb as flasher, add one
transistor and resistor:
Connect one end of original bulb and resistor in series.
If you are using NPN transistor, make sure that resistor is
on negative side of the circuit so you can attach base
to point between bulb and resistor. Connect emiter to other
end of resistor which is actually (-). Your new bulb will be
connected from collector to (+). Note that in order for this to
work, you will have to carefully choose resistor value.
It should have voltage drop ca 0.1-0.2V higher than what is needed
to turn on transistor (this is when original flasher bulb is on).
When flasher bulb is off, current draw will be lower and voltage
drop over resistor will reduce shutting transistor and your bulb off.
Considering component count it is not big deal to make own flasher
circuit using something like 555 chip but this should work fine too.