That is up to the people who are flying them - national flags' guidelines are set by the nations and some are even written into law, but if you're flying a flag of another organization or group, it's up to that group if they want to have guidelines and up to you if you want to respect them. As far as I know, no Pride group has set up official flag protocols, but some other groups that have flags might - most US State flags have their own, and i.e. Reconciliation Australia has guidelines for the Aboriginal flag.

If you're flying another flag along with a national flag, most national flags have a rule that they should be first up and last down, so in theory you should probably take down the Pride flag before you take down the national flag, but then it would be up to you if you want to put it back up, and if you don't have a national flag flying that doesn't apply.

But generally taking down flags at night and during rain is a traditional but widely ignored way to show respect for what the flag represents.