In light of what Wes said:
“Is it generally true that Baptists don't see much continuity with the old covenant and the new? How do Baptists view the promise God made with Abraham?”

I believe that this is a misunderstanding of Baptist CT, though I would agree that that it is generally true among Baptists who hold to a Dispensational hermeneutic.
I thought however, that rather than trying to explain this in my own words (I would probably butcher it), instead I would give anyone who is interested a link to understand Baptist CT.

I must also add that I am not giving this link to stir up anything other than to help people understand Baptist CT.

"The Key to Understanding Scripture" by Dr. Fred Malone