What happens if I flag an answer (or question) and another user does it at the same time (before the flag is addressed by a mod)?
If it's for a valid reason and the post is deleted (moderated) - the flag weight will change for which user? Both?
Flag actions are applied to all users who flag a post, regardless of what they flag it with. Any moderator action such as closing or deleting a post will automatically mark all flags as valid. If the moderator manually marks the flags as valid or invalid, that action applies to all flags on the post.
The one exception is the new "I disagree with the flags on this post" flag, which I believe is only available to 10k users. It's just starting to be used experimentally, but so far, it looks like those flags have an inverse effect: if you flag something as "I disagree with the flags", and the moderator dismisses the other flags as invald, that flag is marked valid, and vice-versa. You really don't need to worry about that though.