Looks like you want to keep you original articles intact but only have /blog for articles that are on your Page named Blog (i.e. You are not using WordPress’s blog home page and not using the usual WordPress loop).
To achieve what you want, you will need to add your own rewrite rules (via functions.php) for the articles you require and filter the specific permalinks for those articles as well. If you group those articles with a category or tag, it would make it easier to do so.
However, if you rather set /blog for all articles in the whole WordPress install (which doesn’t include pages) permalink settings (or even setting a blog page in reading settings) are much easier solutions
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