I host a customisable flair on my website. I wrote the code myself, and it is under the MIT licence. It's more involved than pasting an image into a webpage, but it is a higher quality end product, which is more customisable. It uses the API v 2.2 to get the data. You can change it however you want - move the parts around, chose your own font, change the background colour etc.
To get different information you would have to change the filter value to select the desired information - if people wanted this I'm sure I could add something to implement it!
You can get it here, with usage instructions, or have a look at a live example on my website here, and see where I use it here (scroll down a little).
Examples:
My pronouns are He / Him