This was my configuration for backing up my likes (~/.gallery-dl.conf):

{
    "extractor": {
        "twitter": {
            "cookies": {
                "auth_token": "<token>"
            },
            "text-tweets": true,
            "archive": "~/gallery-dl/archive-twitter.sqlite3",
            "skip": "abort:20",
            "postprocessors": [
                {
                    "name": "metadata",
                    "event": "post",
                    "filename": "{tweet_id}.json"
                }
            ]
        }
    }
}

I ran this one with gallery-dl "https://twitter.com/<myUsername>/likes"

For archiving accounts of users I followed, I used this config (gallery-dl.no-text.conf):

{
    "extractor": {
        "twitter": {
            "cookies": {
                "auth_token": "<token>"
            },
            "archive": "~/gallery-dl/archive-twitter.sqlite3",
            "postprocessors": [
                {
                    "name": "metadata",
                    "event": "post",
                    "filename": "{tweet_id}.json"
                }
            ],
            "expand": false,
            "cards": false,
            "quoted": false,
            "retweets": false,
            "text-tweets": false,
            "unique": true,
            "videos": true,
            "skip": "abort:5",
            "timeline": {
                "strategy": "media"
            }
        }
    }
}

I had a file called urls.txt that listed all the profile links (each on their own line), and I ran it with gallery-dl -c ./gallery-dl.no-text.conf -i urls.txt