I can’t find a font that contains Unicode special character U+266D (music flat sign). I think it should be found among special characters of the Type: Mathematical Symbol. I have the same problem with U+266F (music sharp sign).
You forgot to mention your OS.
On my Linux box (Fedora 30 distribution), most fonts show music signs (flat, sharp and natural). I tried the Liberation, Free and various TeX Gyre families. To be honest, I think they all use the same sub-font because changing the type face does not change the glyphs (just their line spacing or kerning). I must force OpenSymbol to get the “missing glyph”.
Note: the characters are in the Miscellaneous Symbols block U+2600-U+26FF.
Why should they be mathematical symbols? They are in the Miscellaneous Symbols subset.
However, if in the Insert → Special Character… dialog you enter music (as the character names contain that word) into the Search field and then travel the Font list (place the cursor in the combobox edit, not just on the listbox scroll) with the Up and Down cursor keys, you’ll get the available symbols listed for each font as you travel. They’re available for example in the DejaVu family.
(there’s some oddity that sometimes results differ between reaching a font with Up or Down cursor, which seems to be a bug).
On my Linux-Mint Mate system language en-GB, not all the characters show up on the INSERT SPECIAL CHARACTER input. However, if I type the code directly, the characters appear to be there.
To enter musical note with Arial or Times New Roman, for example.
Type the code number then alt-x.
2669 ♩ 266a ♪ 266b ♫ 266c ♬ 266d ♭ 266e ♮ 266f ♯
As @erAck and @ajlittoz pointed out, that character belongs to the “miscelaneous symbols” unicode block. Not all fonts offer that symbol: Libertinus Serif does, but others not. You can enter it anyway using the “unicode toggle” tool in LibreOffice: type 266d and immediately press Alt X. The unicode code will be converted to the right character, and if the font in use does not provide it, LibreOffice will automatically search for a replacement.
Character TeXGyreBonumMath for the text editor.
Character TeXGyreScholaMath for the electronic sheet.
Then “Insert Special character”.