Emergency flashers do flash all appropriate lamps. The left turn signal does work appropriately. The right turn signal does not flash. The right turn signal indicator in the instrument panel remains steady lit when the ignition switch is turned on even with the turn signal lever in the cancelled position.
I recommend you try replacing the flasher unit first to see if that clears the trouble.
Either a burned out bulb (or one not making a solid contact) or perhaps a fault in the multi-purpose switch in the steering column.
I’ve had an intermittent contact problem that sounds similar. The bulb won’t flash, so the turn signal flashes quickly and the indicator light stays lit all the time. All I have to do is fiddle with the bulb to fix my problem.
The most likely culprit is a blown bulb, or else you have a contact/wiring problem. If replacing the bulb doesn’t help, it might be a ground problem or a problem with the flasher.