How may I select a smoothing capacitor to mitigate LED flicker without the use of a scope?
There's a visual difference between flicker and blink...

Flicker (if you can see it) would be something like 40-60 Hz.

Blinking would be much lower, maybe 10 Hz or less.

The difference is important, because flicker can be solved with a cap, but blinking could indicate that there is a bit of a problem that won't be solved with a cap.

For example, the car's electronics could measure the current drawn by the bulb, then decide that the current is too low (because you installed LEDs instead of incandescents) and then decide the bulb is blown, then sleep for half a second, and then restart the cycle. That would result in blinking.

Or the driver chip in your LED bulbs could be "cheap" (ie, braindead), and being driven by PWM pulses could give it a bit of a seizure.

I've had good success with sets of lights by not replacing them all with LEDs, but leaving at least one incandescent bulb. This obviously works only in the case where you got several lights in parallel, but it seems to fool the electronics into thinking that the original bulbs are present. So try this first (ie, one LED, the rest incandescent).

However if the issue is indeed that the PWM frequency is too low, the problem with a capacitor in parallel with the LED bulb is that the discharged capacitor acts like a short and will draw a high current when the bulb turns on, which may cause problems with the switching MOSFET. In this case, a RC network to filter the voltage, may be a better option, or just use a low quality cap with enough ESR to not cause a current spike. 

(for example, using a 0.1R ESR cap in parallel with the lights would cause a 12V / 0.1R = 120A current spike at turn-on... but a cap with a few ohms ESR would be okay)