The expression "becoming adept" is correct and usable in written English.
You can use it when referring to someone learning or developing a skill. For example: "With practice and dedication, Sally is becoming adept at playing the guitar."
Powell himself has not spent all those years in the executive branch without becoming adept at close bureaucratic combat.
This next generation is becoming adept at taking small bits of information, unformed, and assembling it into larger asynchronous maps, of nonlinear order.
They are becoming adept at saying what they don't want, but it's still hard to see where the desire for compromise lies.
Yet we live daily in a web of connections, all of us becoming adept at riding the multiple layers of information.
The delight in all things Japanese came at a time when women were becoming adept at painting china as a hobby.
Still, in laboratories around the world, scientists are becoming adept at breeding animal Methuselahs, extraordinarily long lived and healthy worms, fish, mice and flies.
As communities become more and more familiar with the benefits that prisons bring, they are also becoming increasingly adept at maximizing their windfall through collecting taxes and healthy public service fees.
In addition to becoming scholars in their field, they will become adept at the formulation of testable hypotheses, the planning and execution of well controlled experiments, the thorough analysis/interpretation of data, and the formal presentation of their findings.
Rather than warming to the Fourth Estate, though, the Kirchners are becoming more adept at media manipulation.
The theory that people are becoming more adept in searching the Web is borne out by some hard data, too.
In the 1950s, physicists were becoming more adept at building powerful atom smashers to help decipher the building blocks of matter.
