There's no need to use FQL of batching. This can be done with a simple Graph API request IMHO:
GET /me/groups?fields=id,name,feed.fields(id,message).limit(10)
This will return 10 posts for each of your groups. In case there too much data to be returned, try setting the limit parameter for the base query as well:
GET /me/groups?fields=id,name,feed.fields(id,message).limit(10)&limit=20
Then, you'll get a next field in the result JSON. By calling the URL contained in this field, you'll get your next results. Do this until the result is empty, then you reached the end.