i'm pretty certain it's not a java or flash issue, since those add-ons/extensions are not required to display gif images, something that all browsers have been able to do. i typically run chrome with java disabled, unless it is absolutely required. first thing i would do is to clear your browser cache, close and restart chrome and try again. if that does not help, then run a test with the same site in another (preferably already installed) browser, as someone else has suggested, to isolate the issue to chrome. i typically keep internet explorer installed and "untweaked" (with no add-ons or uncommon settings) to test how a "vanilla" browser would handle certain sites. you could also force ie to run without add-ons.
if it works for you in another browser, then your issue is with chrome. start by checking your extensions (chrome://extensions/) to ensure you're not running any bad extensions that could be hijacking your browser traffic (e.g., malware) or blocking images (e.g., too aggressive ad blocker). if you don't find any bad extensions, check your settings (chrome://settings/content) and ensure that "Show all images" is selected under images and that there are no exceptions, at least none that you would not expect. if none of those work, uninstall and reinstall chrome.
if the other browser also has the same behavior, then your issue is likely with your computer's internet connection or some malware loaded on your machine. check your installed applications (control panel, programs and features) to make sure there isn't anything in there you are not expecting. browser toolbar applications that come bundled with other programs are notorious for hijacking browser traffic and modifying browser settings. also check your internet settings (control panel, internet options, connections, lan settings) and ensure your connection isn't being redirected to a different site/proxy server.