I have lots of these and you can deadhead, to keep them compact and tidy after flowering but I have never found it lengthens the flowering period.

Me neither.

if you chelsea chop them all you do is remove the flowers so they dont bloom at the 'right time' the plant then makes more flowers that bloom later in the year. it doesnt give you a second flush of flowers. so I suppose you can chop some and leave others.

Best time to "chelsea chop" Phlox paniculata is at the end of May, beginning of June (Hence the name Chelsea chop....it should be done when Chelsea flower show is on)

As Phlox are fairly late flowerers, you won't get any joy by doing this now but dead heading is always a good practice.

I dead head mine to keep them tidy after flowering but I have never given them the Chelsea chop as I start getting flowers on mine from June onwards so the chop would be inappropriate for these. I do however give my Phlox subulatas the chop after flowering.