Some had said that flushing DNS could help you stay more anonymous but is this claim legit? I know for sure that webpages can see the DNS servers you're using but could they see your DNS cache? Where is DNS cahce stored anyways? Computer, ISP?
Caching is done in DNS on multiple levels. If a browser queries the (usually automatically) configured DNS server the answer is cached for some time in the browser so that it does not need to lookup again the same domain immediately. It is also cached for some time in the DNS server and if this one has an upstream DNS it is already cached there etc. Such caching means that any clients behind the specific DNS server gets the response faster.
The time to do the DNS lookup for a specific domain could be measured by the page embedding this resource. One could thus find out if a specific user has visited a specific domain recently (cached in browser or OS) or if some user of the same caching DNS server has visited the resource (cached in next DNS server) etc. This could be used to find out which sites gets visited regularly by the user (i.e. which are cached in the browser or OS) and thus create a profile of the user.
The caches could also be used to store user specific results for selected domains in control of the adversary and then detect a specific user depending on the IP address (under control of the adversary) he visits when embedding a resource from this domain. To cite from Technical analysis of client identification mechanisms - Lower-level protocol identifiers:
Such caches can be easily leveraged to store small amounts of information for a configurable amount of time; for example, with 16 available IP addresses to choose from, around 8-9 cached host names would be sufficient to uniquely identify every computer on the Internet. On the flip side, the value of this approach is limited by the modest size of browser DNS caches and the potential conflicts with resolver caching on ISP level.
On the other hand, caching of DNS lookups is important for fast web surfing. Given that there are many other (and often easier) ways to track the user (see again Technical analysis of client identification mechanisms) regularly flushing the DNS will probably not help a lot with privacy.