The reason people use xargs in combination with find is that multiple file names will be passed to the same program invocation of whatever program xargs launches. For example, if find returns the files foo, bar, and baz, the following will run mv only once:
find sourceDir [...] -print0 | xargs -0 mv -t destDir
Effectively, it calls mv like the following:
mv -t destDir foo bar baz
If you don't need or want this behavior (as I assume is the case here), you can simply use find's -exec.
In this case, an easy solution would be to write a short shell script, like the following:
#!/usr/bin/env bash
[[ -f "$1" ]] || { echo "$1 not found" ; exit 1 ; }
P="$1"
F="$( basename $P )"
ffmpeg -i "$P" -f flv "$F"
Save as myffmpeg.sh and run chmod +x myffmpeg.sh. Then, run the following:
find . -iname "*.mov" -exec /path/to/myffmpeg.sh {} \;
This will invoke the shell script once for every file found. The shell script in turn extracts the file name from the full path, and calls ffmpeg with the appropriate arguments.