Firefox does not.
Internet Explorer does not.
There may be hope for Firefox eventually, but until then, things work better if you use ColorSync to convert the image to the Generic RGB profile, then upload to Flickr.
This is fairly straightforward:
- Run ColorSync Utility (in Applications > Utilities)
- Open the relevant image
- In the menus down at the bottom, select “Match to Profile” and “Display > Generic RGB Profile”
- Click “Apply”
- Finder > Get Selected Finder Items
- Preview > Apply ColorSync Profile to Images