I dont find this possibility in the current response types
2 Answers
Yes, it is possible. However, this would depend on the Integration you are using. You may use a custom payload for any rich response of your Agent. If you are using a custom integration, you would have to implement it on your own.
In my end, I have tested it using Dialogflow CX Messenger.
I selected a custom payload in the "Add dialogue option" and followed the format of the payload in the image response type of Dialogflow CX Messenger.
See screenshot below of the test I made in Dialogflow CX Messenger:
Note that images will not show in the console's "Test Agent" section, instead you can only see the JSON when you expand the custom payload tag in the Agent’s response.

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Thank you for the detailed response! It is very useful if you are using Facebook Messenger, however, in my case the integration is with Twilio's WhatsApp, so I'm handling it from the backend. – Guzmán GP Jan 22 '21 at 08:40
Note that the example provided above is for Dialogflow Messenger. Currently, Dialogflow CX doesn't support Twilio’s WhatsApp as a built-in integration. Since you are using your own custom implementation to integrate Dialogflow with Twilio's WhatsApp, you can follow the payload format of the image response type for Twilio's WhatsApp and send it as a custom payload from Dialogflow.
Then in your backend service, you can get the payload from Dialogflow's detectIntentResponse.query_result.response_messages[].payload, parse it and create the valid Twilio's WhatsApp response format before sending it to Twilio's WhatsApp.

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