If you want to add posts web part to your team site – assuming that you have your blog site as subsite (named as “blog“) – you can do this as follows:
1. Create a doc library called Pages, default doc temlate is Web Part Page.
2. Create a page called Test.aspx.
3. Open Notepad, paste following web part code and save this code as Posts.webpart.
4. Change List ID for Posts list in blog site.
Find 43EBBD67-B3EB-4D9F-89C7-B84520A40991 and replace with your blog site’s posts list id.
5. Then, go to your team site web part galleries and upload this Posts.webpart.
6. Add this web part to your Test.aspx.
Now you should be seeing Posts from blog site.
P.S. Before writing this reply, I tested above steps one by one myself and it’s working.
Let me know if you encounter any problems.