JS:

d = { name: "{username}", uh: "{username}", flair_template_id: "{template id}", text: "{new flair text}" };
$.post("https://saidit.net/s/{sub}/api/selectflair", d);

You can get the template id from flairselector. It won't work for me if I click on it, but if I send the request via JS or click the request in the network tab to open it on its own page, you can't edit the flair that way but you can grab the template id from the html.