The original sentence is:
The arrest of the men, who had not yet ordered and were waiting for a friend, kicked off a row over racial profiling.
I search for the "kick off a row", but it only shows "kick up a row", and they seem similar, are they?
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The phrasal verb to kick up merely speaks about to "make" (a row/ noisy argument), whereas kick off implies "starting" it.
The set phrase is to kick up a row, not off.
kick up a row (ODOL)
1.1 Make a vigorous protest.
‘I was quite comfortable—I kicked up a row out of sheer boredom’
However, kick off is another set phrase that means to "start" (something).
kick off (ODOL)
1.2 informal Begin or cause something to begin.
‘the festival kicks off on Monday’
It appears that the writer (cleverly if intentionally) used the two phrasal verbs together.
Incidentally, in BrE, kick off (ibid.) itself means to start a fight:
2 British informal Become very angry; suddenly start an argument or fight.
‘I don't want her kicking off at me again’
In this case, to kick off a row would be tautology.
The phrase in this sentence is "kick-off" it may be british english. It has come to mean start, I guess it comes from soccer where the match is started by somebody kicking the ball (hence that being the first definition). So it could be kick off in this case it started an argument about racial profiling.
it can even be shortened to "and then it all kicked off".
kick-off NOUN 1
The start or resumption of a football match, in which a player kicks the ball from the centre spot.
‘three minutes before kick-off’
1.1 informal The start of an event or activity. ‘the kick-off of the parade’
In this context, they are the same thing. I've not ever heard "kick off a row" or similar - as opposed to "kick up".
I think, as your search shows, it's either much less common, or perhaps it's someone conflating the "kick up" usage with the phrase "kicking off".
To "kick off" or "kicking off" can be used on its own, in this sense to mean getting belligerent, often with violence involved.