I confirm [Daniel Ballinger's solution](http://salesforce.stackexchange.com/a/44800) on this page.

The scope needed for the OAuth token is "web: Provide access to your data via the Web (web)". According to the [Salesforce documentation on Scope Parameter Values](https://help.salesforce.com/HTViewHelpDoc?id=remoteaccess_oauth_scopes.htm), this "Allows the ability to use the access_token on the Web" which I presume means using the Access Token as a cookie?

Steps to download a Rich Text Area (RTA) image via OAuth and curl, or similar programmatic methods:

 1. Make sure you have the correct scope for your OAuth access token. Go to the "Connected Apps" page for your OAuth connected app in Salesforce. Under "API (Enable OAuth Settings)" make sure the scope "web: Provide access to your data via the Web (web)" is included.

 2. If you were using an old refresh token with the old scope, re-authorize and get a new one with the new scope which includes "web".

 3. Get the URL of the RTA image by browsing the Knowledge article and inspecting the image src URL in your browser. The URL should look like

        https://example--c.eu3.content.force.com/servlet/rtaImage?eid=ka0w0000000U2CV&feoid=00Nw0000008eLoi&refid=0EMw00000004lzh

 4. Make a curl request setting your cookie "sid" to the OAuth access token value e.g.

        curl -ik --cookie 'sid=MyOauthAccessToken' 'https://example--c.eu3.content.force.com/servlet/rtaImage?eid=ka0w0000000U2CV&feoid=00Nw0000008eLoi&refid=0EMw00000004lzh'

 5. The request will return a 302 redirect. Do another curl with the redirect URL and set the same "sid" cookie value. Follow 3-4 subsequent redirects, using the returned redirect URL each time, until the response header includes a "Set-Cookie" giving you a new "sid" cookie value.

        Set-Cookie: sid=0023457000079pu!AR8AQO8byIe2NtMi8vd3bt5vVBFqJxgDU2FkQQZd7NgHIQ49CejIVh6FAHyN4mKmSu1UDRAMpWMtUSuAuea0CY123456abcd; path=/; secure

 7. Use the new "sid" cookie value for the next request to the redirect URL.

 8. The request with the new "sid" cookie value will return the binary data of the image in the response body.