There are 2 ways to fix this.
You can install a 2 pole electronic LED flasher in series on the power wire feeding the hazard switch/relay. This works because the Hazard flasher contacts default state is closed when the knob is pulled. Only when a significant load is placed on the relay will the internal spring heat up and break contact to extinguish the bulbs. Once cooled (milliseconds), the spring contact again closes and lights the lamps. This process of opening and closing give you your flasher function. The higher the load, the less "On" time the bulbs will have.
Or you can install a 6 ohm dummy load (resistor) at each tail light signal socket OR each front turn signal socket.
This second option also allows the turn signals to use their original flasher relay. Ideally you would want to find loads that equal about 36 watts including the LED's. A 4 ohm load resistor at 12 volts will draw 36 watts. (LED bulb wattage X 2 + load wattage) However, Bulbs in our cars are 18 watts each and there are also voltage drops in the wiring as well as the peanut bulbs in the dash. A readily available 6 ohm load resistor will suffice. Installing them in front will make them less visible as well as not having to cut any wires. Simply solder them between the lamp socket power and ground wires. The drawback of this setup is they still consume the same power as incandescent bulbs.