I occasionally have the same issue (Windows 10 PC and Chrome). I've just tried again and within the same thread, it looks as though I can like some posts, but not others. The URL that the 'like' links point to are in a different layout:

This won't work: //www.flyertalk.com/forum/#
But this one will: //www.flyertalk.com/forum/british-airways-executive-club/2013951-why-won-t-ba-let-you-get-refund-via-website-5.html#

nb I removed https: from the start of both URLs so that they display properly in this post