My mouth will speak the praise of the LORD,
and let all flesh bless his holy name forever and ever.
Psalm 145 ends in the same manner in which it began: praise. Throughout these verses David has rattled off truth after truth that displays why he is so enamored with the God of Israel. The fact that God is great and, therefore, greatly to be praised is the mantra of this psalmist throughout this psalm. But David is not satisfied with simply his own heart being stirred to song for the beauty and majesty and faithfulness of his God, as wonderful as that surely is. He desires that God receive the worship that is due him, worship from all that is his.
The psalm closes with the psalmist’s promise to praise Yahweh (rsv speak the praise of the Lord) and a call for all people everywhere to bless his holy name for ever (see 106:47). All flesh usually means all human beings; here, in line with every living thing in verse 16b (see also verse 10a), perhaps it means “all creatures” (neb, njb, njv). Let all flesh does not introduce a request for permission but is a third-person imperative. Verse 21b may be rendered in some languages as “Everything that God has created should praise him for ever.”
There are two things that are worth noting. “All flesh” could be, and quite likely is, pointing to not just man and woman but to all of God’s creation. In the beginning, God did not just create man and woman. Not only that, while humans have the unique blessing of being created in God’s image, all of creation was declared good(i.e. without defect and thus without sin) by the one who makes good things. When God stood back from his handiwork he said it was good, in fact it was very good and operated in the manner and to the purpose for which it was created. While humans have a unique responsibility due to being image bearers of our great God, we do not have a unique calling to bring forth praise and proclaim the excellence of God. All of creation exists to declare the wonders of the Lord. Everything exists to praise and honor the one who is ultimately and immanently worthy of boundless praise.
And second, David’s “Let all flesh” is not a request. This is not David begging. It is not a plea. It is a beckon, a summons. David is beckoning all that will hear to Cmon! Come and worship this great King! Extol him! Praise him! Tell of his excellent greatness! David is summonsing the XXX of the King to XXX what is due and you almost hear a hint of incredulity in his voice. You can almost hear in David’s words a, “Why am I even having to encourage you in this? It is the very purpose for which you were made!”
God- the benevolent Sovereign, the just Judge, the merciful Father- deserves all praise, all honor, all glory, for all time. There is not one second of one day where God is not due 100% allegiance, 100% adoration, 100% adulation. David is saying as much. Psalm 145 begins with David expressing why he worships the God of Israel and ends by imploring all creatures of our God and King to render to him the praise that he deserves. There will come a day when all covenant creatures of our great God will bow their knee and confess his Lordship and glory over all. In that day, all of God’s creation will be released from the bondage to which it is presently subjected and will fulfill the purpose for which it was created: to give to God unadulterated and ceaseless praise and honor for all of eternity.
And we will be a part of that creation that praises and honors and enjoys God for all of eternity. CH Spurgeon puts this as well as anyone.
Whatever others may do, I will not be silent in the praise of the Lord: whatever others may speak upon, my topic is fixed once for all: I will speak the praise of Jehovah. I am doing it, and I will do it as long as I breathe. “And let all flesh bless his holy name for ever and ever.” Praise is no monopoly for one, even though he be a David; others are debtors, let them also be songsters. All men of every race, condition, or generation should unite to glorify God. No man need think that he will be rejected when he comes with his personal note of praise; all are permitted, invited, and exhorted to magnify the Lord. Specially should his holiness be adored: this is the crown, and in a certain sense the sum, of all his attributes. Only holy hearts will praise the holy name, or character of the Lord; oh, that all flesh were sanctified, then would the sancitity of God be the delight of all. Once let the song begin and there will be no end to it. It shall go on for ever and a day, as the old folks used to say. If there were two for-evers, or twenty for-evers, they ought all to be spent in the praises of the ever-living, ever-blessing, ever-blessed Jehovah. Blessed be the Lord for ever for having revealed to us his name, and blessed be that name as he has revealed it; yea, blessed be he above all that we can know, or think, or say. Our hearts revel in the delight of praising him. Our mouth, our mind, our lip, our life shall be our Lord’s throughout this mortal existence, and when time shall be no more
 Robert G. Bratcher and William David Reyburn, A Translator’s Handbook on the Book of Psalms, UBS Handbook Series (New York: United Bible Societies, 1991), 1168.
 C. H. Spurgeon, The Treasury of David: Psalms 120-150, vol. 6 (Bellingham, WA: Logos Bible Software, 2009), 382.