In The Complete Jewish Bible translation:

16 The "cup of blessing" over which we make the b'rakhah - isn't it a sharing in the bloody sacrificial death of the Messiah? The bread we break, isn't it a sharing in the body of the Messiah?

17 Because there is one loaf of bread, we who are many constitute one body, since we all partake of the one loaf of bread.

18 Look at physical Isra'el: don't those who eat the sacrifices participate in the altar?

Here is a clip of the Bible Hub's interliner Greek/English of this phrase:

In verse 18, instead of a translation like, "the physical Israel", in the KJV read, "Israel after the flesh". This can convey the idea of two forms of Israel, as if there were the old, natural Israel, the nation, and the new spiritual Israel, the "Church". Once we have this idea in mind, even the translation, "physical Israel", can be used to set out an opposition to a (theologically) "spiritual Israel". There is every reason to realize that this idea never should have occurred to us in the first place.

The New American Standard version has: "Look at the nation Israel..."

The ESV and NIV have: "Consider the people of Israel..."

Most others have essentially the same. These translations can easily convey the same type of idea as the KJV translation.

"According to the flesh" does not need to convey the notion that there are or can be two forms of Israel. Paul could easily be thinking, was surely thinking, "Consider us who are the people of Israel..." In his language, "Israel according to the flesh", he certainly would have been including himself. There would have been no suggestion of a thought of an old versus new and different Israel.