I am using Kitkat - Nexus 5. While sending a message to A using Hangout, how can I insert the contact details of some other person B within the text message to be sent to A...We had this provision in Android 2.2 Froyo itself where it was shown as "Add contact" or "Insert contact" as options within the message itself.
At this time there isn't a way to attach a contact. You would have to copy and paste the details or use a different messaging app. Hangouts is still lacking in many essential features, unfortunately.