Has the church dogmatically declared the meaning of Matthew 16:19. If so what is the document please.
There is not really a set document, but rather a long series of dogmas that are demonstrated to be true, in part, because of the passage.
These include the authority to excommunicate, to bind the faithful to disciplines of worship, to provide indulgences to remit suffering in purgatory, etc. I would recommend researching these topics individually to get a better idea of the meaning of Matthew 16:19.
The footnote in the New American Bible, published by the US Conference of Catholic Bishops, may also provide some additional guidance: usccb.org/bible/matthew/16/#48016019-1
D-R Bible, Haydock Commentary:
Ver. 19. And I will give to thee the keys, &c. This is another metaphor, expressing the supreme power and prerogative of the prince of the apostles. The keys of a city, or of its gates, are presented or given to the person that hath the chief power. We also own a power of the keys, given to the other apostles, but with a subordination to St. Peter and to his successor, as head of the Catholic Church. — And whatsoever thou shalt bind, &c. All the apostles, and their successors, partake also of this power of binding and loosing, but with a due subordination to one head invested with the supreme power. (Witham) — Loose on earth. The loosing the bands of temporal punishments due to sins, is called an indulgence: the power of which is here granted. (Challoner) — Although Peter and his successors are mortal, they are nevertheless endowed with heavenly power, says St. Chrysostom, nor is the sentence of life and death passed by Peter to be attempted to be reversed, but what he declares is to be considered a divine answer from heaven, and what he decrees, a decree of God himself. He that heareth you, heareth me, &c. The power of binding is exercised, 1st. by refusing to absolve; 2nd. by enjoining penance for sins forgiven; 3nd. by excommunication, suspension or interdict; 4th. by making rules and laws for the government of the Church; 5th. by determining what is of faith by the judgments and definitions of the Church. (Tirinus) — The terms binding and loosing, are equivalent to opening and shutting, because formerly the Jews opened the fastenings of their doors by untying it, and they shut or secured their doors by tying or binding it. (Bible de Vence) — Dr. Whitby, a learned Protestant divine, thus expounds this and the preceding verse: “As a suitable return to thy confession, I say also to thee, that thou art by name Peter, i.e. a rock; and upon thee, who art this rock, I will build my Church, and I will give to thee the keys of the kingdom of heaven, the power of making laws to govern my Church.” (Tom. i, p. 143.) Dr. Hammond, another Protestant divine, explains it in the same manner. And p. 92, he says: " What is here meant by the keys, is best understand by Isaias xxii. 22, where they signify ruling the whole family or house of the king: and this being by Christ accommodated to the Church, denotes the power of governing it."
In addition to what runningdude wrote, the First Vatican Council’s dogmatic constitution on the Church (Pastor Aeternus) invokes the “keys” passage in defense of the Petrine Primacy. Strictly speaking, though, I don’t think it solemnly defines a biblical interpretation as dogma, but rather defines the Primacy as dogma, using the verse as proof.