In present internet parlance flex is a noun referring to an ostentatious show of wealth, power, virtue, or some other positive trait. While it's often used as a synonym for bragging my perception is that flexing is typically about something which is evident while the veracity of a brag often relies on the credibility of the braggart. A few examples of a flex would be mentioning how much a possession costs, how much one bench pressed, or how one only eats ethically sourced vegan foods.

Flexing is in principle deliberate, meaning that a fair amount of the discussion about flexing is whether it's actually going on, who it's aimed at, and the intention behind it. A Youtube celebrity flexing on their fans would be in bad taste, two rappers flexing on each other is expected, political candidates flexing on each other is both expected and in bad taste. Being an aspect of negotiating pecking orders it's intensely subjective and contextual how a flex, real or imagined, is taken.