This can be achieved with the first car given to you but will be easier with the faster and more agile cars
There are many jumps all over the Paradise world but there are two locations in the game that this is easiest as it has the largest jumps. The two areas are the Quarry and the near by South Mountain Drive jump.
To initiate a barrel roll you need to hit a split ramp
with one wheel hitting the higher raised side whilst the other hits the normal lower side, once in the air you will need to hold your
in the direction your roll is going to keep the game from balancing out after one roll.
Make sure you have lots of speed and a full boost bar so take a long run up.
Here's a video demonstrating the South Mountain Drive jump, however the Quarry can be seen at 1:12 on the left.