An interesting question. How did you get the "flat" character into your question?
I found it in two fonts that are installed on my Win 7 system, Arial Unicode MS and Lucinda Sans Unicode:
I was unable to find a way to map a keyboard key to a Unicode value, and this article suggests that it can't be done: https://github.com/kiibohd/KiiConf/issues/30 (but see "Further research" below).
As a possible alternatives to using Charmap, or if you don't have either of the two fonts I mentioned, see this: https://www.johndcook.com/blog/2008/08/17/three-ways-to-enter-unicode-characters-in-windows/
The Unicode Input utility is described here https://www.fileformat.info/tip/microsoft/enter_unicode.htm and downloaded from here (about mid-way down the page) https://www.fileformat.info/tool/unicodeinput/index.htm
This is overkill, but I guess not enough people thought that $169 was worth it: http://www.photologic.ca/unicode_keyboard.htm
Further research:
https://scripts.sil.org/cms/scripts/page.php?site_id=nrsi&id=uniipakeyboard