It varies somewhat.

For your own blog, you set the rules about crossposting.

Communities often but don't always state rules about crossposting. Some want whole fic, others just a thumbnail description and links. Most allow crossposting, but some discourage or ban it. The lower traffic, the more likely crossposting is welcome; the higher traffic, the less likely. For the most part, posting to your blog and one other topical community is fine.

There's a whole entry about crossposting here.