When I want to check how many flags per day, I have to either calculate it (which is frustrating because the number is constantly changing) or wait until either the new day starts or I use up all of my flags (so I get the "You have X flags remaining" message). It would be much easier to either have at the bottom of the flag box, "You have used X of your Y flags today" (instead of "You have X flags left today") and/or have the flagging page show this information.
But a lot of users might find this useful, and I don't see any downside to this.
Well then, since several people have tried to explain the downsides to you in comments, allow me to put those downsides in an answer, so those downsides won't be hidden when the comments collapse, and everyone (not just you) can easily see them. But there are very good downsides to be mentioned, and very good reasons to not show that number directly to people.
or I use up all of my flags (so I get the "You have X flags remaining" message)
First, I'll correct a serious misunderstanding of the system. On any site where you're not a moderator, you will always see the 'You have X flags remaining' message. So you don't have to use up any flags, nor do you have to use up all flags, just to see that message.
It would be much easier to either have at the bottom of the flag box, "You have used X of your Y flags today"
It wouldn't, because right now people can scan for a number and immediately know they have the right one. Having two numbers there would require more reading and parsing of the message, and thus it wouldn't be easier.
It would also add noise, like I stated and Glorfindel too: The only number relevant is the one that let's you know how many flags you have left before you run out.
and/or have the flagging page show this information.
The flag page is there to show you which of your flags are still pending, and which ones were handled. It shows you which of your handled flags were helpful and which were declined, so you can educate yourself on how to flag properly. The flagging page is not an 'achievement' list, the information on how many flags you 'unlocked' doesn't belong there.
You show quite a bit of misunderstanding when it comes to flags, like in this comment:
Also badges show their progress so this privilege is harder to know your progress then a badge is.
In fact, 'amount of flags per day' isn't an achievement, or a privilege to be unlocked. There is no progress to be measured, since there is no goal. A badge or a next privilege level are goals, so that's why their progress can be tracked. An extra flag a day isn't a goal.
As Catija neatly explained, showing the number anywhere would only encourage people into unwanted behavior.
Even your own response and reason for wanting this number mentions you've already falling victim to it! All "Flagging to increase flags" does is create empty busy-body work for moderators. Moderators have limited time, energy and attention spans too, and if we use it on handling stuff that doesn't really need handling, we might not have any left when there is stuff that really needs handling.