Step 1: Free download FLV to MOV Converter and install it.
The interface is like the following:

Condition1: you already have flv video files on your computer.
1. Click file button, choose the flv video you want to convert
2. In output format, Choose quicktime (MOV).
3. Click start convert FLV to MOV.
Condition2: Want to directly convert FLV to MOV online.
Here we take youtube for example, if you want to convert FLV from youtube to MOV, it is very simply.
1. Click URL Button, copy the url to this FLV to MOV to Converter, for example: copy the url
http://www.youtube.com/watch?v=Xz3CkM0QdK4&feature=dir
2. In output format, Choose Choose quicktime (MOV).
3. Click Converte to start convert FLV to MOV. For More Information See this Guide: How to download youtube videos