Add a link to download photos and videos from Instagram. (http://i.imgur.com/RvyxF2u.png)

InstaDownloader.user.js

// ==UserScript==

// @name     		InstaDownloader
// @description		Download photos and videos from Instagram.
// @include  		https://www.instagram.com/p/*
// @require  		https://ajax.googleapis.com/ajax/libs/jquery/2.1.4/jquery.min.js
// @require  		https://gist.github.com/raw/2625891/waitForKeyElements.js
// @version	 	1.1
// @license		GPL v3 or any later version (http://www.gnu.org/copyleft/gpl.html)
// @grant    		GM_addStyle

// ==/UserScript==


function addDownloadButton(jNode) {
	// Left align the download button
	$('.t28').css('align-items', 'flex-start');
	
	var downloadButtonText = '';
	var downloadLinkURL = '';
	
	// Check the type of media
	var medium = $('meta[name="medium"]').attr('content');
	if (medium == 'image') {
		downloadButtonText = 'Download Image'
		downloadLinkURL = $('meta[property="og:image"]').attr('content');
	} else if (medium == 'video') {
		downloadButtonText = 'Download Video'
		downloadLinkURL = $('meta[property="og:video"]').attr('content');
	}
	
	// Create download button
	var downloadLink = document.createElement('a');
	downloadLink.setAttribute('id', 'downloadLink');
	downloadLink.setAttribute('href', downloadLinkURL);
	downloadLink.innerHTML = downloadButtonText;
	
	// Add the download button to page
	$('.t28').prepend(downloadLink);
}

waitForKeyElements('div.s28', addDownloadButton);


/* Style our newly added elements using CSS */
GM_addStyle ( multilineStr ( function () {/*!
    #downloadLink {
	    -webkit-appearance: button-bevel;
        -moz-appearance: button-bevel;
        appearance: button-bevel;
        padding: 7px;
        margin-bottom: 4px;
    }
*/} ) );

function multilineStr (dummyFunc) {
    var str = dummyFunc.toString ();
    str     = str.replace (/^[^\/]+\/\*!?/, '') // Strip function () { /*!
            .replace (/\s*\*\/\s*\}\s*$/, '')   // Strip */ }
            .replace (/\/\/.+$/gm, '') // Double-slash comments wreck CSS. Strip them.
            ;
    return str;
}

Firefox 85.0b4 (64-bit), Tampermonkey 4.11.6120 - no links or buttons for downloading appeared, everything in the context menu is as usual.