Mine also is not working it seems. I noticed yesterday on my Arqade profile that it was not rendering (fixed now with my band-aid fix mentioned below).
I did notice just now however that if I take the link and upload it as you would when posting images on a post, it seems to pull it down just fine.
My flair's .png link "https://stackexchange.com/users/flair/8729580.png" does not render an image, but after uploading it via link it does:
Of course, it doesn't properly navigate you to my SE user profile since the link behind the image is for the image itself.
peterh's .png link does not work for me either, but again, uploading it does.
To top it all off, Luuklag's .png like works for me.
So a (temporary?) fix for this would be to take your .png's link and upload it to i.stack.imgur and then change your flair
<img src="https://i.stack.imgur.com/M02q6.png" width="208" height="58" alt="profile for Timothy G. on Stack Exchange, a network of free, community-driven Q&A sites" title="profile for Timothy G. on Stack Exchange, a network of free, community-driven Q&A sites" />
I think though the only drawback to this is the image won't get updated as your reputation changes.