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I am not quite sure if I understand your concern correctly. What would be JotForm's part on this? You mentioned you would like to embed OAuth2 to a 3rd party API? I'm sorry I'm not sure how this is setup in your end.
If you want to integrate JotForm to your web app, you can simply use our API. Here's our documentation on it: http://api.jotform.com/. Perhaps your question might be answered in our developers forum? You can check it here: http://developers.jotform.com/forum
I want to explain more details about it.
I want to insert a hyperlink into a jotform that will embed an authorization OAuth2 request to 3rd party API (http://developer.teamsnap.com/documentation/apiv3/authorization/#web-application-flow). After user input credentials to grant access to 3rd resources, jotform will get response access_token from the url parameters (redirect_uri of OAuth2) and post that access_token to another url (google web apps url).
Is it possible?
From the quick overview, I think what you want is to integrate your form with teamsnap, although I'm not sure how teamsnap works. Yet, I do think it's possible what you would like to achieve.
You can add a URL to your webhook so all form submissions will submit there as well. Then on the URL that is set on your webhook, should be the end that processes your submissions to teamsnap. Then that's how it should also submit to teamsnap from JotForm.
You can learn more about webhook from this user guide: http://www.jotform.com/help/245-How-to-Setup-Webhook-with-JotForm
But for additional information and more expert advice, we recommend to post your inquiries as well at http://developers.jotform.com/forum.