How can I create this look in FCP?

Hello I would first copy main layer above to a new layer make the new layer black and white and reduce opacity to about 50% (basic bleach bypass). This will desaturate your image some. Then make a new layer and add a gradient with colors orange, green, and red and reduce opacity so colors appear dull over video and add a soft blur. Blur might also look better added to black and white layer instead.
Then make a new sequence and add a 3 frame small black slug video about every 4 seconds to the sequence. Also add a 2 frame white slug every 3 second or so. Add this sequence to the main sequence and reduce the opacity to about 20%. This should give you the sudden jumps in brightness and darkness I see in the video.

Or you could just use a Nattress Film Effects effect. :)
 
A slug is simply a placeholder of sorts. It just fills a gap of space w/ black video basically. To find it go to your Effects tab. Then go to Video Generators. The Slug 'effect' is in there. You don't apply it to a pre-existing clip, simply drag it onto the timeline and you'll see what it is.

cheers.
 
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