At present, the current way to use these queues is to either leave feedback using the canned comments, (which get written on the post by the Community user), mark the post as "Looks Ok", or edit the post in question. You can also perform an "Other Action" (see below) to also finish the review item.
You can flag the post if it needs it, but currently this will not allow you to complete the review task, leaving you in a weird position of having to still either leave feedback using the canned comments, or mark it as ok/edit it - all of which seem awkward to do after flagging the post.
There are a lot of improvements planned for these new queues, as discussed on the SE Meta site. There is a helpful answer of all the implemented/planned/rejected bug fixes and feature requests for the new queues on the post. I encourage you to check it out, as it is quite a lot to repeat here.
The biggest issue (in my opinion) that is currently being planned can be seen here - this deals with the flagging awkwardness I mentioned earlier.
Looks like the options now are the following:
The main change being the "Other Action" option, which will automatically be selected if you:
- Flag the post
- Vote to close (questions only)
- Comment on the post
- Upvote on an existing comment
- Vote on the post