I quit using Google a long time ago, and went to Bing search. That’s where I found the gif of the Gadsden flag you’re asking about.
Seems to me, if the image were being systematically purged from the web, Google and Bing would be the last places you’d find it, but they both have tons of them.
Thanks for checking. Ixquick searches Google and other engines itself and usually comes up with tons of images no matter what the search. To get the ‘no documents of that description’ message for both ‘gadsden flag’ and ‘don’t tread on me, flag’ (and variations thereof) just amazes me. Not even the commercial postings of it, which obviously exist, come up.