Is there a standard time duration before DNS caches are cleared?

You'll be happy to know that most (if not all) DNS server software has protection against this scenario.

For example:

Microsoft DNS server has a MaxCacheTTL setting, which defaults to 86400. So regardless of any TTL setting in DNS RRs, if this is not adjusted, the DNS server will not cache anything longer than a day.

BIND also has a similar setting max-cache-ttl, which defaults to 604800 (7 days).

PowerDNS alao has the setting max-cache-ttl and defaults to 86400.

Unbound names the setting cache-max-ttl and defaults to 86400.

Since BIND is still the most popular DNS server out there, its 7 day default will affect you. If you find out this has happened, you'll probably have to wait a week before most everyone has flushed their caches.