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There is a couple of possible problems. What typeface is it and what format? Most of the fonts in the Adobe Fonts service are in OpenType format, but a growing number are available in OpenType Variable format. A few are even in OpenType-SVG (aka color fonts). As far as I can tell Flexi and most other "CAS" applications do not support Variable Fonts or Color Fonts. Adobe Illustrator, recent versions of CorelDRAW and even Inkscape do support variable fonts. If you added a variable font it's probably not going to show up in Flexi's font menu. Or if it does show up it might act like variable fonts do in Affinity Designer: show only a basic instance of the font or lots of copies of the same instance (Serif needs to get it together with its font handling).
Another likely issue: you might have "added" a type family at the Adobe Fonts website, but haven't "installed" it for all apps to use yet. Recently Adobe made some big changes to the functionality of Adobe Fonts. Previously you could do everything at the Adobe Fonts website. When a new type family was added the default behavior was to make that type family available for all applications on computers signed into your CC account (and even a mobile device like an iPad). Now when you add a type family at Adobe Fonts that type family is only initially available to Adobe CC applications. You have to open the desktop Creative Cloud application and go to its Fonts section in order to install it for all applications to use. I don't really like this extra step. One reason is because it's a pain to scroll through the list of added fonts. The scroll bar keeps disappearing. I have to use the scroll wheel of my mouse. At home I use a Wacom tablet; it has no scroll wheel, so I have to use the arrow keys on the keyboard. Like I said, it's a pain.