I didn't know about James McCartney or Zak Starkey, but I knew the others are musically talented. The only work I've heard from them is Dhani's contributions on George's final album, Brainwashed, and Concert for George.
James McCartney played on his father's
Flaming Pie album back in '97.
Dhani also contributed guitar on the Traveling Wilburys' remasters to finish up "Maxine" and "Like a Ship." I believe Dhani also played guitar on his father's last recorded song, "Horse to Water," as his father was too weak at the time to do anything but provide vocals. I'd like to see Dhani (George Harrison's son) record with Norah Jones (Ravi Shankar's daughter), just because I think that would be cool.
Zak Starkey, as mentioned, was Oasis' drummer for
Don't Believe the Truth, but he was sacked by Noel for
Dig Out Your Soul. (I'm not sure what the reason for the sacking was, but Starkey had said in interviews prior to that that he really felt unnecessary in Oasis as Noel is a multi-instrumentalist.) Starkey has also been with The Who since the early 90s, though he was unable to record
Wire & Glass or
Endless Wire because of his Oasis touring commitments. In neither case -- Oasis and The Who -- was Starkey an official member of the band; though Pete Townshend has invited Starkey to become a permanent member of the band, which Starkey has declined.
Lennon's sons have had musical careers that go back a long ways. Sean Lennon recently composed the music for
Rosencrantz and Guildernstern are Undead.