Can I integrate Jive with any other open source framework or application server? Like if I want to access my activity streams from any other application/framework/portlet then what are the different ways to achieve this?

Your question is a bit vague, but in most cases the answer is yes. You can access the API

https://developers.jivesoftware.com/api/v3/cloud/rest/index.html

Via HTTP Basic or Oauth and then translate the information into your framework.

Again it depends heavily on the capabilities of the calling platform as well.