I like to download videos, you never know when something will disappear or move and who wants to watch 30 ads surrounding a video suck more bandwidth and make the video buffer?
But I've found it's a never-ending battle to download videos. Everyone keeps changing formats and in some cases deliberately taking steps to make downloading the videos (especially from web services made specifically to do it) not work.
The streamed videos are the most challenging. I've found in most cases VLC can download a streamed video though but it's NOT user-friendly and the wizard often does not work and you have to do it manually.
In any event, finding the URL to download can be tricky and involve sometimes a lot of headache viewing a page source.
I don't use instagram so I don't have any site-specific advice for you other than to say it'll be a never-ending battle.
I work for the Department of Redundancy Department