I doubt you need to add diodes to the circuit to get it to work. LEDs are different than incandescent light bulbs; they will only flow current in one direction. My first guess would be that you've got them wired up backwards. Check for polarity markings, or just try reversing them.
The usual problem with LED lights is that they don't draw enough current to get the flasher to turn off, so instead of blinking, they'll just stay on continuously. Some people will add resistors in parallel with the lights so they'll draw enough current to make the flasher work correctly, but that seems ridiculous to me -- one of the nice things about LED lights is that they draw less current, which conserves power, which is especially nice on an EV (though in reality, the amount of power saved is extremely small overall). A far better solution is to simply replace the flasher with a more modern one which doesn't need high current to operate correctly. There are some vehicles which actually measure the current draw to determine when a light bulb goes out, in which case it makes some sense to use an external resistor, but the Zeros don't.