Reporting reposts, edits, etc. on other sites.
To answer the earlier question: you must be a representative of the copyright owner (artist) or the copyright owner yourself in order to report something submitted to Instagram. This is because the only apparent reporting method is through filing a DMCA notice, just like on tumblr. However, it appears this notice must be e-mailed, as there's no form like tumblr and deviantART have. (dA's requires an account to use because dA is full of dumbfuck mods, but I digress.)
In my experience of filing DMCA notices in the past, most sites will accept screencaps showing that the artist granted you permission to file the notice on their behalf. Still, it is usually best to have the artist file it. deviantART, for example, considers third-party reports the lowest priority, which is why nothing ever seems to get removed. Reports filed informally by the artist ("My Work Used") or filed formally through their DMCA form are the highest priority.
The only problem with getting the artist to report however is that DMCA notices require personal information and certain statements in English.
"I have a good faith belief that the disputed use is not authorized by the copyright owner, its agent, or the law."
"Under penalty of perjury, I state that the above information in this notice is accurate and that I am the copyright or intellectual property owner or an authorized person to act on the copyright or intellectual property owner's behalf."
No site, I've found, has been considerate enough to translate their form or instructions into different languages; not everyone is comfortable providing their personal information either, especially when someone writing in a different language links them to a form requesting the info. It would be nice if someone more well-versed in Japanese and other languages could write up a guide for non-English speakers about what the DMCA is and how to fill it out notices correctly so we could show it to the artists when telling them about reposts, edits, and theft.
Each time a DMCA notice is found valid, the person being reported should receive a warning about it. I know on tumblr and deviantART they certainly do. It is common practice on sites that multiple valid DMCA notices filed against someone will eventually result in that person's account being suspended or permanently banned. If you really want to do damage to the editing/render/theft/reposting community, DMCA is the way to go.