No, there are none other than the three Kinslayings we know of.
Thereupon Fëanor left him, and sat in dark thought beyond the walls of Alqualondë, until his host was assembled. When he judged that his strength was enough, he went to the Haven of the Swans and began to man the ships that were anchored there and to take them away by force. But the Teleri withstood him, and cast many of the Noldor into the sea. Then swords were drawn, and a bitter fight was fought upon the ships, and about the lamplit quays and piers of the Haven, and even upon the great arch of its gate
(Of the Flight of the Noldor)
But Dior returned no answer to the sons of Fëanor; and Celegorm stirred up his brothers to prepare an assault upon Doriath. They came at unawares in the middle of whiter, and fought with Dior in the Thousand Caves; and so befell the second slaying of Elf by Elf. There fell Celegorm by Dior's hand, and there fell Curufin, and dark Caranthir; but Dior was slain also, and Nimloth his wife, and the cruel servants of Celegorm seized his young sons and left them to starve in the forest.
(Of the Ruin of Doriath)
And so there came to pass the last and cruellest of the slayings of Elf by Elf; and that was the third of the great wrongs achieved by the accursed oath.
For the sons of Fëanor that yet lived came down suddenly upon the exiles of Gondolin and the remnant of Doriath, and destroyed them. In that battle some of their people stood aside, and some few rebelled and were slain upon the other part aiding Elwing against their own lords (for such was the sorrow and confusion in the hearts of the Eldar in those days); but Maedhros and Maglor won the day, though they alone remained thereafter of the sons of Fëanor, for both Amrod and Amras were slain.
(Of the Voyage of Earendil and the War of Wrath)
There were perhaps some very small conflicts between, for example, the Avari and the Sindar or Noldor, or something along the lines of what happened with Eol in Gondolin, but no other instances of Elf-on-Elf warfare are recorded other than the Kinslayings you mention - and the third is supposed to be the "last" slaying of Elf-by-Elf.
It is known that Morgoth had enslaved some Elves to his will (which is why escapees where never trusted), so there may have been further individual instances of Elves murdering Elves. There was certainly never anything on the scale of a civil war, excepting the Kinslayings.