I have been flagging answers where I have removed cursing so that mods are aware of a user in the case they violate the rules on a regular basis. Should I not flag it after I have removed the cursing?
Whether a flag is needed depends on whether you think the issue merits moderator attention.
The Stack Exchange system is designed so that many of the moderation tasks can be handled by a community of high-reputation users. If it looks like editing the question solved the problem, then moderator intervention would be unnecessary. On the other hand, if there appears to be a pattern of abuse that the moderators should be aware of, then please do flag it.
There are some actions that moderators can take, if we decide that a user's contributions are not welcome. For example, we can send a stern warning to the user, impose sanctions such as temporary bans, or in extreme cases disable the account altogether.
There's no need to flag every time you remove cursing. You should only flag if there's a problem that requires moderator attention. Individual cases of cursing does not warrant this, especially as it can be simply edited out if it's bad enough.
If you've been noticing it from a particular user, and they refuse to stop if it's indeed a serious matter (excessive cursing that's not at all constructive), then you can flag for moderator attention, and they'll deal with that user if necessary.