1) Katarina - 80% (4/5)
Of the five episodes Adrienne Hill was in, only one survives, making her the Most Burninated Companion.
=2) Sara Kingdom - 77.8% (7/9)
Again, the sad loss of three quarters of The Daleks' Master Plan means we have only two episodes of Sara.
=2) Ben and Polly - 77.8% (28/36)
This number goes down a bit if you drop episodes in which they did not appear; neither was in episodes 4 and 5 of The Faceless Ones and Polly gets a week off in Power of the Daleks, all of them missing episodes. Their only intact story is their first, The War Machines.
5) Victoria - 70% (28/40)
I'm counting from her debut in the second episode of Evil of the Daleks to the end of Fury from the Deep. Like Ben and Polly, she has only one intact story, Tomb of the Cybermen.
6) Steven - 63.0% (29/46)
Like Katarina and Sara, a victim of the Season Three purges, but more fortunate in that three complete stories survive - The Time Meddler, The Ark and The Gunfighters. (Also his first appearance in the last episode of The Chase.)
7) The Second Doctor - 52.9% (63/119)
Yep, fewer than half of the Second Doctor's episodes remain, and only six complete stories out of 21. The losses are particularly bad in Seasons Four and Five (as evidenced by the higher rankings of Ben, Polly and Victoria above). Troughton gets a couple of episodes off but it doesn't affect his ranking.
8) Jamie - 50.4% (57/113)
Since there were only six Second Doctor episodes without Jamie, and they are all missing, his percentage is slightly lower.
[Parenthesis: of the twelve black-and-white episodes with Colonel / Brigadier Alastair Gordon-Stewart, precisely half survive and half are lost - he is not in the first episode of either The Web of Fear or The Invasion. However at this stage he is a recurring character rather than a regular on the show.]
9) Dodo - 42.1% (8/19)
Not a particular favourite of most fans, Dodo none the less got off lightly in the Season Three purges, with only one of her full stories (The Savages) being completely wiped.
10) The First Doctor - 34.3% (46/134)
The spread is very uneven with only 11 episodes deleted from the 81 of the first two seasons, but almost two thirds of the remainder lost, including his last one. Hartnell took more time off than Troughton, but again this won't affect his ranking.
11) Vicki - 28.2% (11/39)
Vicki does better at the start than the end of her era: only two episodes out of 30 are missing from her first seven stories, but then the final nine (counting Mission to the Unknown, which of course she isn't actually in) are all lost.
12) Zoe - 20.8% (10/49)
Season Six has survived better than the other Second Doctor stories, and five of Zoe's eight stories are intact. (And we don't weep too much for The Space Pirates.)
13) Susan - 17.6% (9/51)
Almost all of the first run of stories has survived, the only casualties from Season One being Marco Polo and two episodes of The Reign of Terror.
=14) Ian and Barbara - 14.3% (11/77)
The Coal Hill school teachers benefit from the relative survival of Season One, and even more so from Season Two, where only two episodes of The Crusade are missing. Proportionally Ian and Barbara are the best represented of the early regular characters, making them jointly the Least Burninated Companions (of those who were burninated at all, of course).
Odd that the beginning and end of the black and white era have survived relatively well; it's the middle that has been hollowed out. One can always hope for a few stray finds in someone's garage or attic to rebalance the odds.