I have found the HTML to show the flair, and I was wondering if it was possible to place this in a LinkedIn profile.
Where would be the best place to put it?
You could place your flair within a Google Presentation embedded in your LinkedIn profile. Check my profile:
Here's a blog post I wrote about it:
[ Update ]
LinkedIn has revamped their profile editing features and now it's possible to add a link that points directly to your StackOverflow flair. Just click the "Add a link to a video, image, document, presentation." Then enter your flair URL. Mine is this one (replace the last part with your StackOverflow user id):
The good part is that the flair image reflects your current rep (is updatable) and so is a great win over the older Google Presentation method where the image wouldn't be updated.
In new LinkedIn profile layout you can add "media" to each block. I've added url to my flair in my summary block and account url to it's description. Here You can see how it looks like:
Turns out that miniature created by SO isn't refreshed. So to see Your actual score You have to click on the content and view it as a "popup window". I would be happy with some better way to do this.
It is refreshed, but only periodically.
Are you able to hotlink to an image on a LinkedIn profile? If so, this might be kind of a duplicate of "Can we get flair as an image?"
The first answer there includes one user's implementation of image-based flair, since there is no official solution. But if you're unable to hotlink to an image, then this wouldn't help.