Super easy to get without having to buy, upgrade or tune anything. You could also unlock the following achievement if you continue to accelerate after unlocking Flat Out:
What you need to do is from the main menu go into:
Free Play > Hot Lap > Bugatti > Veyron 16.4 > Le Mans > Old Mulsanne Circuit
The plan is to reach four full bars of speed* on the extremely long straight. Just drive like you normally would for the first section and when you get on the straight floor it.
It'll take a while to get up to the intended speed but you will eventually reach it, most likely on your first attempt.
*about 300-350KMH (~210MPH) if I remember correctly