Movie or TV show with a flamethrowing badguy and a deathtrap car that raises taunting signs [closed]

Your description very well matches the episode "The Widowmaker" of MacGyver Ep. 8 Season 3.

From IMDB:

While scaling the cliff face known as "The Widowmaker," Mac loses his best friend. Before he can properly grieve, he is forced to run from an old enemy who is now hunting him down. With the help of a colleague, Mac finds his way back to the Widowmaker and fighting for his life on the same ledge that took his best friend.

Commenting your description:

Except the engine wouldn't start. On one side of the car, a mechanical flag (I was young; this is what it registered as) went up, with some sort of taunt or warning.

It was attached to the wipers and read "Bye bye time to fry." :)

Then one showed up on the other side. After that, the radio display turned into a time bomb countdown.

It wasn't the radio, while struggling to escape the Jeep, MacGyver noticed a beeping sound from a timer. His colleague Nikki Carpenter asked "what's that noise?". It was audible from inside the engine compartment, only the camera showed the timer but MacGyver was sure it's "bad news". There was no other flag though.

Our hero tries the door handles, which are now inoperative. He's trapped! Eventually he kicks out a window of the vehicle and runs away before it blows up.

In fact, he was able to kick out the windows, both escape the Jeep before it explodes.

Here's one key scene:

(Source: The MacGyver Project)

Here's a short cut on Youtube (showing some scenes you're looking for): MacGyver - The Widowmaker