I think that the OP has got "series" and "parallel" mixed up. The LED lamps will have a series resistor or some other current control device, or they would fail when 12 V is applied.
There is another resistor in parallel to take current that is approximately equivalent to that of an incandescent bulb. That current will fool the car's systems into thinking that the indicators are working.
The problem is that the car is attempting to detect the incandescent bulbs with a very short duration pulse, that is too short to cause a bulb filament to get red hot, let alone white hot as it would be when lit. The LED lamp responds instantly and lights briefly.
What is needed is something to slow down the turn-on of the lamps by a few milliseconds, so that the LEDs don't come on. I suggest a relay. For an ordinary automotive relay, connect terminal 30 to ground, terminals 87 and 85 to the indicator feed wire, and terminal 86 to the LED indicator. Leave the load resistor connected to the indicator feed wire, not the LED indicator. You need to do this for each side of the vehicle.
When the indicators come on, the relay will operate and light the LED. However, there should be a sufficient delay that the very short bulb testing pulse will fail to operate the relay, leaving the LED off.
You should be aware that the resistor that fools the car's system into thinking that the indicators are working means that you won't get any warning if the LED indicators fail, and that a working bulb failure system for indicators has been a legal requirement for decades in most countries.