First, you can always write an editor for a journal and ask him/her to consider you as a reviewer for certain topics.
Second, it is certainly appropriate to ask your post-doc advisor, the next time he/she requests that you review a paper that he/she has been assigned, to instead ask the editor to invite you to directly. This way you start to get credit for reviewing manuscripts. I think most supervisors would be willing to do this for post-docs. Just argue that it's important to you to start establishing yourself as an independent scientist.
As to how beneficial it is... well, it's not going to make or break you, but you can use it as evidence of independence when it comes to applying for full time positions. And if you are reviewing papers anyway, you might as well try to get the credit for it.