When I encounter spam in the VLQ queue, I go to the post and flag it as spam, as you do. Then I click Skip in the queue.
After several Looks OK reviews, a post is dropped from the queue, preventing other reviewers from seeing it. Spammers want people to see their spam, and normally it's good to prevent this. But in cases where the people who are seeing it are likely to flag it, which definitely includes the LQP review queue (because people using that queue have accounts, are interested in deleting posts that don't belong, and usually want to serve their community), it is better for those people to see it. I think it is best that spam posts remain in the VLQ queue until they are deleted.
I do not think the value of preventing the spam from being deleted for the wrong reason (i.e., by "Delete" or "Recommend Deletion" reviews) outweighs the value of making people aware of it who are likely to flag it. Unless hard numbers exist that can justify clicking Looks OK on spam posts, I do not recommend doing so. Furthermore, if that did turn out to be more effective at stopping spam, it would indicate that the review and/or flagging systems we have are pretty badly broken, and the best ultimate solution would be for Stack Exchange developers to put a "Flag as Spam" button in the review queue, or to make other adjustments.
I said I click Skip, but actually there's an exception to this: if I know the spam has already been deleted by the time I get back to the review item, I'll go ahead and click Delete. There's no need to do so, though, and arguably it would be better if I still clicked Skip, since the number of reviews we can do per day is limited. Once the spam post is deleted, it really doesn't matter much how you review it, so I wouldn't worry about that. But I recommend clicking Skip on spam that hasn't been deleted yet, so that more reviewers will see and flag it.