Need help with the strumming patterns for this piece (fly me to the moon)

He is throwing in some triplets, it is a little busy for my taste, but it is excellently played.
There are many ways to play a triplet. Look for tutorials on you tube and find one that works for you.
To me the key is being able to get in and out of the strum.
 
Yes, also note that Fly Me To The Moon in the versions most of us know was arranged for a Bossa Nova rhythm (it was originally called "In Other Words" and in waltz time). So looking up some youtube videos of Bossa Nova strums for ukulele might give you further insight.

Welcome to the forum!
 
I appears to be that the ukulele in the recording is tuned to D6 tuning...so if you are trying to play along with the fingering that you see—and it sounds wrong—you know what is going on.

Do you have the sheet music to this arrangement? There is a lot going on in the strumming pattern...

-There is a shuffle strum, or swung strum
-There is a triplet strum—which this player plays like a “fan” strum
-There is individual picking of melody notes

And I am not judging, but there are a couple of times where he stops strumming (the hand freezes) or he plays a single strum.

I would use YouTube to slow down the video (maintaining the pitch) and play along (if you have the sheet music).

If I were going to take it apart to teach you (again, if there was music), I would separate the chords from the melody and practice each separately. We’d do the chords on a shuffle strum, and then add the triplets where desired. Separately, we’d look at the melody. And then finally, we’d slowly put it altogether—one of us playing the melody, the other playing the chords. And this would all be done in and out of tempo and slower/faster as needed.

You could record yourself playing the chords and then play the melody along with your recording.

Ultimately, what I would say to everyone is this: you could be Jake Shimabukuro, too. You can play anything that he plays if you learn the songs, piece by piece, and then speed up over time. He just happens to have played ukulele since he was 4 and has incredible head start on most of us (30-40 years) and he grew up in a place that has always accepted ukulele, where as the the mainland United States had a pretty closed mind about ukulele for nearly 40 years (as a folk instrument at best)...which, incidentally, Jake’s Strawberry Fields YouTube video in 2006 had a role in changing.

So...take your time, have patience, and master what you want to master. Focus on what you can do and what is just out of your reach—and when you conquer that—add the next piece.

Good luck!
 
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