So, it was me, who had too much free time to count the flashbacks. Or at least those in FotR and TTT EE. And the final count is 16 (If I haven't forgotten anything).
Here they are:
FotR:
- Prologue
- Bag End: Gandalf talking to Frodo: flashback to Gollum in Barad-Dur
- Rivendell: fb to Gandalf's escape
- Rivendell: Elrond talking with Gandalf: fb to Isildur and Mount Doom
- Anduin: the gift-giving scene
TTT:
- Gandalf fights the Balrog
- Rohan: Aragorn tracking the hobbits: flashback to Pippin at the orcs' camp
- Rohan: Aragorn tracking the hobbits: 3 separate flashbacks -> hobbits meet Treebeard
- Fangorn: 3 Hunters meet Gandalf: fb to Gandalf fighting the Balrog
- Going to Helm's Deep: Aragorn's dream flashback to Arwen in Rivendell
- Going to Helm's Deep: Eowyn talking to Aragorn: fb to Elrond conversing with Aragorn and Aragorn conversing with Arwen ("our time here is ending...")
- Rivendell: Elrond talking with Arwen: flashforward to Aragorn's death
- Ithilien: Faramir thinking: Faramir sees Boromir's boat floating by
- Ithilien: Faramir thinking: the victory of Osgiliath
What do you say about that?