To elaborate on Caterwaul's point: the compatibility chart (presumably you're referring to this one
) covers the inter-compatibility between MMS1st bodies and Shinki using that body and the newer MMS3rd body. However, if you're only taking parts from two MMS1sts or two MMS3rds, they're almost certainly going to be compatible. If you don't know which body a given Shinki is, you can look at the compatibility chart; any sets listed on the left-most column are MMS1st sets. Alternatively, you can usually tell by looking at the body; the MMS3rds are in general curvier, with the most noticable difference being the hip joints; MMS3rds have more rounded and organic-looking hip joints than MMS1sts. Also, the MMS3rd body comes in two sizes; Tall, which is about the same size as an MMS1st, and Small, which is about a head shorter. MMS1sts only come in one size.
On chest plates specifically: between the MMS1st and MMS3rd figures, the design of the chest changed significantly. MMS1sts have chest plates that snap onto the front, while MMS3rds have vest-style chest plates that go over the shoulders and latch on both in the front and back. There does exist an adapter to mount MMS1st chests on an MMS3rd, but it's rare and makes the chest plate stick out more than it should.