The creation of stackapp has been accepted shortly after
On Stack Exchange anyone with sufficient reputation can create a tag. There is nothing for anyone to approve or accept with that. Both stackapp and flair were created by you on your question, and then both tags were removed from your question through an edit by another user.
I will not answer your questions about the tag deletion because you already know who deleted it and they already gave you their reason for doing so. Additionally, I find the question about tag creation more interesting, because what was done here in the first place was that two new tags was created.
How/where can I veto this decision? Only here on meta? Every time such happens?
I wouldn't call it "veto". The only veto available here would be if a moderator locked the question, or blacklisted a tag. But generally, yes, meta is a good place for discussions about tags. Every time it happens? Hopefully it will not happen that often. If disagreement about new tag creation would happen that often, there would be a bigger problem.
Unlike Wikipedia, where there's no (to my knowledge) limit on how many categories can be applied to a page, and each category can have multiple sub-categories: On Stack Exchange you are limited to 5 tags per question, and there is no tag hierarchy system (despite several suggestions to introduce one). This means that tagging questions on Stack Exchange is not the same as categorizing Wikipedia pages. There are similarities of course, but there are also major differences.
Without proper categorization/tagging you're lost on big sites like these. You're not going to find anything. And if, you're not going to find it easily.
Are you comparing the size of Code Review Stack Exchange with that of Wikipedia? Flattering, but on Code Review we have as of this writing 43 657 while Wikipedia has over five million pages (and that's only on the English version of Wikipedia). Searching for stackapps or flair is quite easy here and it's also possible to filter it to only questions or only answers.
About the tags themselves
Let's take a look at your proposed tags and how many other questions could use them:
Four questions in total found when searching for "flair". Out of these, only one other than yours could use the tag, and it was asked six years ago.
Five questions, including yours, would be appropriate for the tag "stackapps". However, all of them are also appropriate for "stackexchange", which is a slightly broader tag. As already mentioned, Stack Exchange doesn't have a tag hierarchy system. Introducing the tag could lead to tag fragmentation (If we add "stackapps", should we also add a tag for the SEDE - Stack Exchange Data Explorer?)
When reading your question I thought of a previous meta question about when to create a new tag for a game. @rolfl had some good things in his answer there, specifically:
- For askers, they connect experts with questions they will be able to answer - they allow you to direct your question to the people most able to answer it.
- For answerers, they are for sorting your questions into specific, well-defined categories. You can follow tags, get updates on changes, even mails and other notifications.
- Tags can be used to report on broad statistics, tracking activity over time, etc.
- Tags can be used for awarding badges.
- (...) There has to be an expectation of a reasonable, and continuing number of questions that will be candidates for the tag. Will there continue to be a need for the tag?
Now let's ask some questions related to your proposed tags:
- Are there 'flair' experts that would like to follow the tag?
Probably not that many.
- Is there an expectation of a reasonable number of questions that will be candidate for the 'flair' tag?
Given what I mentioned before, two questions in six years, no.
- Are there 'stackapps' experts that would like to follow the tag?
Given the broad variety of Stackapps, I'd argue that it's hard to be an expert in that area. However, there are definitely experts of Stack Exchange, to which there is already a tag.
