According to the US Navy Regulations of the era, a "captain of the fleet" had practical command of the fleet by giving his flag officer's instructions to its several vessels, like an executive officer to the Admiral or flag officer, who was busy commanding a fleet rather than the several component vessels. That appears to have been the job of the Captain of the fleet when so designated.
From the 1841 US Navy Regulations...
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In action, while the flag officer is paying attention to defeating the enemy, the Captain of the Fleet pays minute attention to the several vessels of the fleet, and communicates and records the orders etc. and the movements of the vessels...
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From the 1870 US Navy Regulations... should a fleet commander fall, the Captain of the fleet might assume command if aboard the flagship, until the next officer in seniority to the flag officer should assume charge...
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