The Flex offence became popular during the late 1950s and early 1960s, but was known then as Reverse Action. Pete Newell, the great coach of California University who also coached the 1960 US Olympic team, was credited with developing the Reverse Action offence. Reverse Action went out of fashion for some time as coaches favoured methods that emphasised individual athletic talents and less screening situations, but during the mid 1980’s it became popular again under a new identity: the Flex.
The Flex offence is a continuity offence requiring all players to be effective using cuts to a low post position, using screens to create mid-range or 3pt scoring opportunities and one-on-one penetration. Like all similarly structured offences, it is possible to include variations to the basic screening and cutting options to exploit individual talents.

4 looks to pass to 3. 1 sets a down screen for 5.

The above action can then continue from the right side of the floor.

2 flex cuts off 3 and 4 sets a down screen for 3.
If the ball is passed to the wing, a common action is to look for a pass to the post and an away stagger screen.

1 and 4 set a stagger screen for 2.

2 cuts off the stagger screens looking for a shot.
4 slips to the ring.
Many offensive schemes feature a flex cut action but may not use the flex, as it was originally designed, as a continuity offence. Many NBA teams will incorporate a flex cut and the screen the screener action. Here is an example from the Boston Celtics and their coach Brad Stevens.