Wheat -
the OT doesn’t equate Israel directly to wheat but the NT does use this idea of wheat and barns with regards to the elect or those who believe on Him, who hear his voice, and follow Him.
Let both grow together until the harvest: and in the time of the harvest I will say to the reapers, Gather up first the tares, and bind them in bundles to burn them; but gather the wheat into my barn.
The wheat is the Word of God. The only those who live by the Spirit can produce the fruits of the Spirit.
“Now the parable is this: The seed is the word of God.”
Luke 8:11
If the wheat remains in us (the flesh, the chaff) then it can produce much fruit but only if we remain in the vine and allow the Spirit to flow into us because apart from Him we can do nothing. We have to remain IN HIM.
“If you abide in me, and my words abide in you, ask whatever you wish, and it will be done for you. By this my Father is glorified, that you bear much fruit and so prove to be my disciples.”
John 15:7-8
There is also another reference to wheat/grain also in the context of the New Covenant
““For surely I will command, And will sift the house of Israel among all nations, As grain is sifted in a sieve; Yet not the smallest grain shall fall to the ground.”
Amos 9:9
Other translations say not a pebble will fall which indicates that it’s a pure house of Israel or a true grain without contaminants. Hence the wheat or the grain in this case is referring to the restored house of Israel or the booth of David or the Church of Jesus Christ under the New Covenant.
Chaff -
this is referenced multiple times in the OT and it was always in relations to those who are either God’s enemies/the nations, are not adherents of God’s Commandments or the wicked.
The wicked are not so, But are like the chaff which the wind driveth away.
The nations shall rush like the rushing of many waters: but he shall rebuke them, and they shall flee far off, and shall be chased as the chaff of the mountains before the wind, and like the whirling dust before the storm
Then was the iron, the clay, the brass, the silver, and the gold, broken in pieces together, and became like the chaff of the summer threshing-floors; and the wind carried them away, so that no place was found for them: and the stone that smote the image became a great mountain, and filled the whole earth.
This text you quote from parallels in the OT from a combination of places.
Let them be as chaff before the wind, And the angel of Lord driving them on.
This title is specific to Jesus and here John the Baptist is equating Jesus with the Angel of the Lord.
Therefore they shall be as the morning cloud, and as the dew that passeth early away, as the chaff that is driven with the whirlwind out of the threshing-floor, and as the smoke out of the chimney.
This speaks about Efraim who in Hosea is one with the nations due to their certificate of divorce that God gave to the Northern Ten Tribes but which God would restore
Notice that the first example was not about wheat and chaff but about bearing fruits and trees.
Even now the axe is laid to the root of the trees. Every tree therefore that does not bear good fruit is cut down and thrown into the fire.
This is repeated in the sermon on the mount by Jesus Himself
The sermon starts in chapter 5:2 and it ends in chapter seven with several illustrations, the wide and narrow way, the house on the sand and on the rock and the bad and the good fruit tree.
If one’s righteousness does not exceed the righteousness of the Pharisees he will by no means enter into the kingdom of God.
“Every tree that does not bear good fruit is cut down and thrown into the fire. Thus you will recognize them by their fruits.”
Matthew 7:19-20
And Jesus explains who the good fruit trees are.
“"Not everyone who says to me, 'Lord, Lord,' will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven.”
Matthew 7:21
If you want to be a good fruit tree that has good fruits then it’s a matter of submitting to the will of the Father and living by the Spirit.
But the bad tree which produces bad fruits are those who live according to their own righteousness, they walk the broad way and build on an uncertain foundation of the Law. They attempt to attain entrance via their good works and unfortunately God’s imputed righteousness is the only acceptable means to entering into the kingdom.
So the chaff is a reference to anyone who produces bad fruits, lives by the law, attempts to gain right standing with God through their own works, enter through the wide gate, walk the wide and easy road, build on a sandy foundation and will be destined for burning and removal.
You risk complicating things when you say that the chaff holds the wheat.
True it does but no one enters via the works of the flesh. Even the wheat sheds the chaff. Even the righteous shed their mortal bodies and take on the immortal predestined glorified bodies.
In this case the distinction should be between the wheat that has grain and that which has none. When all is said and done, the empty wheat is chaff and the full wheat after separating the wheat out is also chaff. So unless there is something that carries over, it all burns up. And those who live by the flesh will have no good fruits or no wheat or no house left standing.