After A/B testing, here is what I ended up using:

  instrumentName = \markup \concat { B \raise #0.8 \magnify #0.6 \flat " Major"}

Adding the \magnify property to the \concat string resized the flat to my 
satisfaction. Thanks for the help!
________________________________
From: lilypond-user-bounces+piercello=hotmail....@gnu.org 
<lilypond-user-bounces+piercello=hotmail....@gnu.org> on behalf of David 
Kastrup <d...@gnu.org>
Sent: Tuesday, January 3, 2023 11:52 AM
To: Matthew Pierce <pierce...@hotmail.com>
Cc: lilypond-user@gnu.org <lilypond-user@gnu.org>
Subject: Re: flat symbol in text?

Matthew Pierce <pierce...@hotmail.com> writes:

> How might I display the text "Bb Major," but with the flat symbol
> instead of a lower case "b"?

I'd just use Unicode, namely "B♭ Major".  If you don't get this via
input methods (on my keyboard, it's "[Compose key] # b"), you can
copy&paste from a browser with Unicode tables or from this mail
message...

In contrast to LilyPond's \flat, this will be a text font flat, usually
fitting better with the text font.  If the text font has it, of course.

--
David Kastrup

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