Where to store the refresh token on the Client?

You can store encrypted tokens securely in HttpOnly cookies.

https://medium.com/@sadnub/simple-and-secure-api-authentication-for-spas-e46bcea592ad

If you worry about long-living Refresh Token. You can skip storing it and not use it at all. Just keep Access Token in memory and do silent sign-in when Access Token expires.

Don't use Implicit flow because it's obsolete.

The most secure way of authentication for SPA is Authorization Code with PKCE.

In general, it's better to use existing libraries based on oidc-client than building something on your own.

You can store both tokens, access and refresh, as cookie. But refresh token must have special path (e.g. /refresh). So refresh token will be sent only for request to /refresh url, not for every request like access token.