You can embed images you've hosted on Dreamwidth in your own journal, in other journals, in communities, in comments, and on other Livejournal and Livejournal-based sites like InsaneJournal, but Dreamwidth does not allow images to be embedded on other non LJ-related sites. Discord probably has a similar policy (though since they don't seem to have the hosting space issue Dreamwidth has, I don't know why), and I have no idea what Nickpic's deal is.