What do you mean by 'scrub through'?
If you mean that you want to remove the fast forward/rewind controls, or the bar which shows the current progress through the movie, you can simply use an alternative skin for your FLVPlayback component.
Assuming you're creating your instance of the FLVPlayback component on the stage from within the Flash IDE, the easiest way to do this would be to select the instance of the component on the stage and open up the component inspector window by selecting 'Window->Component Inspector' in the main menu or by pressing Alt + F7.
In the 'Parameters' tab of the component inspector window, click on the 'skin' property and then select the magnifying glass, this will bring up a dialog which will allow you to select a different skin for your component, so you could choose one of the more basic skins which has only the play/pause button and the mute button (with no progress bar, volume control or FF/RW buttons).
Alternatively, you could select 'none', so your FLVPlayback component will have no controls on it. If you set the autoplay property to true, your movie will play from start to finish as soon as it has loaded, but the user would have no way to control the playback, so you'd have to control/monitor playback via actionscript if you wanted to allow the video to be played again.
Otherwise, if you really want to you could have a go at creating your own skin and using that. Offhand, it's been a while since I did any serious flash development, so I can't remember too many of the details with regard to reskinning the FLVPlayback component, but you should be able to find tutorials online which covers this.
I seem to recall it wasn't particularly difficult to do when I tried, but I can't remember the exact process. It was a long while ago now! (back when Flash 8 was new!)
Anyway, I hope that is of some use.
Cheers for now,
Jas.