I don't believe that.
First, he is probably not writing it himself. He can barely manage a 140-character tweet without errors in spelling, punctuation, and grammar.
Second, he reads little and relies heavily on ghostwriters.
Third, the content of JFK's inaugural is at odds with what Trump has said. Compare and contrast:
JFK: We observe today not a victory of party but a celebration of freedom--symbolizing an end as well as a beginning--signifying renewal as well as change.
Trump: I mean think of it. We won a landslide. That was a landslide. And we didn’t have the press. The press was brutal. You know what? Hey, in the great state of Ohio, we didn’t have the upper echelon of politicians either, did we?Founding Principles
JFK: And yet the same revolutionary beliefs for which our forebears fought are still at issue around the globe--the belief that the rights of man come not from the generosity of the state but from the hand of God.
Trump: The world is not fair. You know they come with this statement "all men are created equal." Well, it sounds beautiful, and it was written by some very wonderful people and brilliant people, but it's not true because all people and all men [laughter] aren't created—now today they'd say all men and women, of course, they would have changed that statement that was made many years ago.Standing Up to Aggression
JFK: Let the word go forth from this time and place, to friend and foe alike, that the torch has been passed to a new generation of Americans--born in this century, tempered by war, disciplined by a hard and bitter peace, proud of our ancient heritage--and unwilling to witness or permit the slow undoing of those human rights to which this nation has always been committed, and to which we are committed today at home and around the world.
Trump: But, you know, the people of Crimea, from what I've heard, would rather be with Russia than where they were. And you have to look at that, also. Now, that was under -- just so you understand, that was done under Obama's administration. And as far as the Ukraine is concerned, it's a mess. And that's under the Obama's administration, with his strong ties to NATO.Pay Any Price
JFK: Let every nation know, whether it wishes us well or ill, that we shall pay any price, bear any burden, meet any hardship, support any friend, oppose any foe to assure the survival and the success of liberty.
Trump: If we cannot be properly reimbursed for the tremendous cost of our military protecting other countries, and in many cases the countries I’m talking about are extremely rich. Then if we cannot make a deal, which I believe we will be able to, and which I would prefer being able to, but if we cannot make a deal, I would like you to say, I would prefer being able to, some people, the one thing they took out of your last story, you know, some people, the fools and the haters, they said, “Oh, Trump doesn’t want to protect you.” I would prefer that we be able to continue, but if we are not going to be reasonably reimbursed for the tremendous cost of protecting these massive nations with tremendous wealth — you have the tape going on? ... With massive wealth. Massive wealth. We’re talking about countries that are doing very well. Then yes, I would be absolutely prepared to tell those countries, “Congratulations, you will be defending yourself.”Allies
JFK: To those old allies whose cultural and spiritual origins we share, we pledge the loyalty of faithful friends. United, there is little we cannot do in a host of cooperative ventures. Divided, there is little we can do--for we dare not meet a powerful challenge at odds and split asunder.
Trump: Oh sure, I know that. I mean, I understand what’s going on, I said a long time ago — that NATO had problems. Number one it was obsolete, because it was, you know, designed many, many years ago. Number two — the countries aren’t paying what they’re supposed to pay.Foreign Aid
JFK: To those new states whom we welcome to the ranks of the free, we pledge our word that one form of colonial control shall not have passed away merely to be replaced by a far more iron tyranny. We shall not always expect to find them supporting our view. But we shall always hope to find them strongly supporting their own freedom... If a free society cannot help the many who are poor, it cannot save the few who are rich.
Trump: It is necessary that we invest in our infrastructure, stop sending foreign aid to countries that hate us and use that money to rebuild our tunnels, roads, bridges and schools—and nobody can do that better than me.South of Our Border
JFK: To our sister republics south of our border, we offer a special pledge--to convert our good words into good deeds--in a new alliance for progress--to assist free men and free governments in casting off the chains of poverty.
Trump: When Mexico sends its people, they're not sending their best. They're not sending you. They're not sending you. They're sending people that have lots of problems, and they're bringing those problems with us. They're bringing drugs. They're bringing crime. They're rapists. And some, I assume, are good people.The United Nations
JFK: To that world assembly of sovereign states, the United Nations, our last best hope in an age where the instruments of war have far outpaced the instruments of peace, we renew our pledge of support--to prevent it from becoming merely a forum for invective--to strengthen its shield of the new and the weak--and to enlarge the area in which its writ may run.
Trump: The United Nations has such great potential but right now it is just a club for people to get together, talk and have a good time. So sad!Sacrifice
JFK: And so, my fellow Americans: ask not what your country can do for you--ask what you can do for your country.
Trump: I think I've made a lot of sacrifices. I work very, very hard. I've created thousands and thousands of jobs, tens of thousands of jobs, built great structures. I've done, I've had tremendous success. I think I've done a lot.Citizens of the World
JFK: My fellow citizens of the world: ask not what America will do for you, but what together we can do for the freedom of man. Finally, whether you are citizens of America or citizens of the world, ask of us here the same high standards of strength and sacrifice which we ask of you. With a good conscience our only sure reward, with history the final judge of our deeds, let us go forth to lead the land we love, asking His blessing and His help, but knowing that here on earth God's work must truly be our own.
Trump: There is no global anthem. No global currency. No certificate of global citizenship. We pledge allegiance to one flag and that flag is the American flag. From now on it is going to be: America First. Okay? America first. We're going to put ourselves first.