I've been searching ages for this, so I'm going to answer this question myself...
How do I use and reference system environment variables in a flyway configuration file?
You have to add the env. namespace before the envar name, and wrap it in ${env.MY_ENVAR_NAME}.
Example:
Setting up an exemplary environment variable, e.g. in bash
export MY_ENVAR_KEY=MY_ENVAR_VALUE
Using the environment variable in the flyway.toml
...
[environments.dev]
url = "jdbc:snowflake://something.snowflakecomputing.com/?db=SOME_DB&warehouse=SOME_WH&role=SOME_ROLED&schema=SOME_SCHEMA&authenticator=snowflake_jwt&private_key_file=path/to/snowflake.p8&jdbc_query_result_format=json&private_key_file_pwd=${env.MY_ENVAR_KEY}"
...