I am not sure if this helps, but if I output:
print_r( openssl_get_cert_locations() );
I get the following:

This suggests that PHP/Guzzle is looking for certificates in my C:\Program Files\Common File\SSL\cert.pem, opposed to WordPress’s included cert. I tried renaming and adding the ca-bundle.crt to that directory and restart Local, but it still hasn’t resolved the issue.
I based the above find on this suggestion on StackOverflow.
Perhaps there is some way of incorporating the contents of ca-bundle.crt into Flywheel’s own certificate?