In the Text and Button elements, you have font management options. The drop-down with fonts shows 5 popular Google fonts and your theme fonts (the list of fonts will vary from theme to theme).
The theme fonts are provided just as font families, without the styling they have inside the theme (not as font styles: Heading 1-6, paragraph, etc). You have full control over the size, letter spacing, and line-height to achieve any styling with these fonts – similar to font styles or custom.
If you want to add a custom font to use it in Flex Block, you need to add this font to your theme typography (there is no need to style it when you add it, since it will be pushed to Flex Block without the styling as mentioned above). After it’s added to your theme typography, you need to save your current progress within Flex Block and refresh the page where you are working with Flex Block (in case you don’t need to save the updates, just refresh the page) – you will see the new font inside the list of your theme fonts.
Check the tutorial about adding Custom Fonts here.
If you have any issues with your text/fonts inside FlexBlocks, check this list with the most common issues here.