The phrase "a flex of" is correct and usable in written English.
It can be used to describe a display of strength, power, or confidence, often in a boastful or showy manner.
Example: "He made a flex of his new sports car, showing it off to all his friends."
Alternatives: "a show of" or "a display of".
I looked the buffalo straight in the eye and with a flex of my muscles, I charged like the warrior I had trained to be, sprinting and screaming with the spear ready to strike.
It has to be said that the cross Lennon put over was David Beckham-quality in its execution, requiring Gerrard only to come in at the back post and dispatch the ball with a flex of his neck.
The Reyhanli bombings were a flex of Bashar al-Assad's military muscle, which is bolstered by a region-wide array of loyal proxies with a reach far beyond that of the Syrian Army.
Third set, Nadal* leads Berdych 6-3, 7-5, 4-3: With a shuffle of feet and a flex of forearm, Rafa Nadal scurries into the backhand side to lash a lethal south-paw forehand, inside-out, to the far corner of the court.
That way I can skip to the next song with just a flex of my pecs, since reaching up to push the button would make it look like I'm scratching myself…".
I put one bag on my lap, another around my neck with my keys in my mouth, as I click the lock button with a flex of the jaw.
It may even be seen as a flexing of Cameron's newly bulging muscles.
This summer, though, has also brought a flexing of muscle by the Premier League's middle class.
But now, more than ever, the notion of the fashion object as museum piece seems little more than a flexing of narcissistic muscle.
Here the ball is delivered with a huge flick of Mr Muralitharan's rubbery wrists and, according to many observers, a flexing of his elbow.
When the shaped ski is tipped on its edge and pressured with a flexing of the ankles and knees, the sidecut carves a definitive, C-shaped turn in the snow.
