Here is quick overview from Wikipedia that gives you an idea about where DNS caches reside:
However, the Linux TCP/IP stack does not come with a DNS cache. So if you want to cache DNS request on a Linux system, you will need to install a DNS resolver with caching function. Popular examples are: nscd, dnsmasq, unbound
Manjaro doesn’t seem to use any of these and therefore doesn’t seem to have a DNS cache in the OS layer:
Your applications (for example browsers) might still come with their own DNS cache. I would not expect applications to cache DNS requests on disk (for performance and other reasons), so you can likely flush the application’s DNS cache by restarting the app.