The famous riff of this one quite lends itself to uke. After playing the B chord, lift your index finger to play the open strings and the hammer on (H indicates hammer-on).

         H     H     H     H      
         |     |     |     |      
A|-2-2-----0-----0-----0-----0---
E|-2-2-0-2---0-2---0-2---0-2-----
C|-3-3---------------------------
G|-4-4---------------------------

[riff]
[riff]

I was [riff] born in a cross-fire hurri[riff] cane
And I [riff] howled at my ma in the driving [riff] rain

But it's [D]all [A]right [E]now, in fact, it's a [B]gas!
But it's [D]all [A]right, I'm [E]Jumpin' Jack Flash
It's a [B]gas! Gas! Gas!

[riff]
[riff]

I was [riff] raised by a toothless, bearded [riff] hag
I was [riff] schooled with a strap right across my [riff] back

But it's [D]all [A]right [E]now, in fact, it's a [B]gas!
But it's [D]all [A]right, I'm [E]Jumpin' Jack Flash
It's a [B]gas! Gas! Gas!

[riff]
[riff]

I was [riff] drowned, I was washed up and left for [riff] dead
I fell [riff] down to my feet and I saw they [riff] bled

I [riff] frowned at the crumbs of a crust of [riff] bread
I was [riff] crowned with a spike right thru my [riff] head

But it's [D]all [A]right [E]now, in fact, it's a [B]gas!
But it's [D]all [A]right, I'm [E]Jumpin' Jack Flash
It's a [B]gas! Gas! Gas!

[riff]
[riff]

Bonus tips from Maurice Rickard:

Drone out on B with the A string open, and alternately fingering the E string and leaving it open. This gives you the open-tuning feel of original in the outro.

For an extra bit of flair, play this right before the D in the chorus instead of playing the last iteration of the riff:

A|--2--2--2--2--0--0--0--0--0
E|--2--2--2--2--2--2--2--2--2
C|--3--3--3--3--3--3--3--3--3
G|--4--4--4--4--4--4--4--4--4