First of all, it looks like you're strumming with your thumb. Is that true?
I find it nearly impossible to chuck with a thumb strum. I use my index finger nearly all the time. I strum over about the 12th fret, and I keep the finger nice and relaxed and "noodley".
Try this: Play a simple DUDUDUDU strum with your index finger over the 12th fret or so. Nice and steady. Nothing fancy.
You could (if you wanted) count out the beat as you play. Out loud or in your head:
One and Two and Three and Four and
One and Two and Three and Four and
Notice that your "down" strums are on each number (one, two, three, four). Your "up" strums are in between the numbers, on the "ands".
Next, forget about strumming for a bit and treat your uke like a percussion instrument (maybe a bongo drum?) Keep your hand where it would be for strumming, but instead
hit your uke on the strings and body with your palm. Your thumb should be more or less parallel with your top string during the hit. The base of your wrist will be over or near the soundhole.
Do the count again (One and Two and...), hitting the uke on beats two and four:
One and (hit) and Three and (hit) and
One and (hit) and Three and (hit) and
Remember, you're not strumming yet. You're just playing your "Bongo Uke" on the correct beat.
So far, so good, eh? Now you just have to put the two things together.
It's true that you'll be strumming down with your index finger and immediately muting the strings with your palm. But
don't think about it that way! You'll just go crazy trying to coordinate everything.
If you simply do the index finger strum and the "my uke is a bongo" trick
at the same time, as if two different people were playing (a strummer and a drummer), then the "chunk" will occur automatically, as a natural byproduct of the process.
Nothing about your strum should change. Nothing about your bongo-uke-playing should change. They'll just both be happening together, using the same hand, on the same ukulele.
That's how I think about it, anyway. Might help you. Might not.
JJ