Fast Seek has no effect for FLV files
From at least 2.2.0 to the 20180625 nightly of 3.0.4 the Fast Seek option has no apparent effect on FLV files.
Seeking in large FLV files can take up to 5 seconds per hour of video from an HDD. Three mostly empty HDDs were tested and the results were the same for all of them. Playing back large FLV files burned to optical discs is much, much slower.
The FLV files tested include a variety of old downloads from YouTube and very recent captures of HDS streams.
VLC appears to be parsing all data from the current position to the seek position. This is the default behavior of FFmpeg and presumably Libav as well. This is due to the lack of an index in FLV files.
Seeking quickly in FLV files is certainly possible even without an index. FFplay can seek anywhere instantly in FLV files when seeking by byte offset instead of time is enabled by using "-bytes 1" on the command line.
Libav apparently has the following function for seeking by byte offset that may be useful:
int64_t avio_seek(AVIOContext *s, int64_t offset, int whence)
All testing so far was done with: XP SP3 32-bit / Athlon II x4 645 / 6 GB.