We only support authorization code flow for external identity providers.
However, as you are setting up an Okta-to-Okta connection, all you should have to do is create a Web app in the Org that you are using as the Identity Provider (the Source org, as that is where the user was created and has credentials). These values will then be used when you create the IdP in the Target org (the org that these users need to log into)
Your actual app that the users in this Source/IdP org will use will actually be created in the second (Target) Okta org (the one in which you configure/create the Identity Provider), and that one can be a SPA. Your React app would then use the client ID for the SPA app in your Target org and users from both the Source org AND the Target org will be able to login