You don't need anyone's permission to write, but you do need a subject and a milestone. Narrowing in on your subject is deeply connected to performing your literature review (see questions on LR). Reading published work will attune you to the concerns and norms that matter in your field. As you read, keep a list of open questions.
Developing writing skill takes time, so don't assume that you can rush through it. Outlines are crucial, because without them, you won't know what you are writing. Always seek feedback: peers or friends can reveal both important problems and new angles of attack.
The ultimate test of accomplishment in academic writing is publishing journal articles (see questions on publications). While you might not need this achievement in hand to enter that PhD program, insofar as publishing is a main goal of academic endeavor, you can expect to work on it later on. Therefore, your proximate goal could be to produce writing similar in tone, finish, and advancement to what you see in your field's main journals.