Yes sometimes flights do get delayed due to thunderstorms if the thunderstorm is too severe to fly in.
If it's just rain and a slight thunderstorm then the flight may go on without delay but if there are any severe thunderstorms that are forecast within 20 to 30 minutes of the flight taking off or a tornado is in the forecast then the flight may be delayed or even cancelled and rescheduled for the next day or so when the weather is cleared up.
If the thunderstorm is severe enough then yes the flight will get cancelled due to the bad weather conditions.
Some thunderstorm a plane can safely fly in but if the thunderstorm is too severe they will cancel the flight and reschedule the flight until it's safe to fly again.
They will watch the weather closely and when the weather clears up they will reschedule that flight until then.
Such as if a tornado is coming then yes the flight will be cancelled but if it's just a small thunderstorm that goes away soon then they will wait the flight out and then take off on the flight when the weather is clear enough.
I've had a few flights that I was flying on cancelled due to the thunderstorms that was severe enough but then again I just had a few flights delayed a few hours until the stormed passed by.
But always be prepared to have your flight either delayed or cancelled when thunderstorms are in the forecast.