A couple things play into this from a logic standpoint, which is all I have to go on with this question since it isn't really covered in the historiography. This isn't to say that OP's question is a bad one at all, though, it's just that fighting at night wasn't something most commanders of this era considered as feasible, hence there isn't much writing on the subject. I'll hit on a few points like (1) the intended use of flares in the American Civil War [ACW], (2) battle tactics, and (3) army logistics.

So to start, let's talk about the way the illumination rockets or flares were used during the ACW. All the accounts I have read about the use of flares do indeed align with naval operations, as OP said. However, except for signaling purposes ship to ship, flare or rocket use was usually something that defenders used in fixed positions so as to determine enemy movement. For example, when Grant ordered Adm. Porter to run his boats past Vicksburg in the dead of night (this was late March 1863), he was trying to sneak past the defenders. The Confederates had devastated Union boats that had tried to run past them in the past, as there was a hairpin turn in the Mississippi River just in front of the rebel works at Vicksburg (essentially giving the Confederates two shots at anything trying to get past). When Porter and Grant tried to sneak by in the middle of the night, the Confederates launched rockets to illuminate the night and spot targets, and took their best shots (it didn't matter, nearly all the Union boats and transports got through). This kind of operation represented the majority of rocket/flare operations during the ACW: spotting encroaching foes trying to sneak closer to or by someone. Which brings us to tactics.

(2) It would not have been in a commander's interests to launch a flare or rocket ahead of offensive operations, as it would advertise an attack in advance. The only reason to launch an attack at night would be to take advantage of darkness for concealment and surprise purposes: launching a flare so troops knew where they were going would negate both advantages. Thus, to attack at night using flairs would not have been practical. The light would have been temporary anyway, and unless a steady barrage of illumination rockets were used, it would have been nearly impossible for regiment commanders to keep their units in line with supporting elements, and even more difficult for division commanders to make adjustments based on the development of the fight (it would have been nearly impossible to see more than a few dozen yards ahead). Couriers would have been in danger of being mistaken as enemy units at night (ask Stonewall Jackson about that), so any communication between friendly forces would have been VERY difficult, even if you could keep a steady stream of rockets firing to provide adequate illumination for hours at a time. Which brings us to:

(3) Army Logistics. It would have been very difficult getting troops that had fought all day to engage in offensive actions at night as well. This would represent anywhere between 12-18 hours of steady, non-stop fighting. Even if you gave your troops a break at nightfall, then ran them in again at midnight, you're asking a lot of troops that weren't used to fighting in this way. Conversely, if you held some units back during the day specifically so you could pitch them in at night, you're facing an enemy during the day with one hand tied behind your back. If there was no fight during the day, why go at night when you could just wait until the morning? If surprise was really what you are going for, see above in tactics: you're going to lose that surprise when you start firing rockets ahead of your attack. Lastly, as it concerns logistics, it would have been very difficult to set up for this kind of attack. You'd have to travel with wagons upon wagons full of illumination rockets, then get them set up in the right place for an attack at night. Even if you were able to keep something like that secret (which would have been difficult since it would have been such a to-do to pull off), how could you possibly know a day or two ahead of time exactly where the lines would be set (so you could set up your hundreds of rockets)? Outside of a siege operation, most battles in the ACW were very fluid, and involved surging back and forth between lines or locations. In the instances where people were set in their lines, and they knew where the attack was coming from (i.e., Petersburg, Battle of Nashville, etc), a surprise attack wouldn't have done much good. Defenders were dug in, and waking them up with a bunch of flares just before the attack wouldn't have provided the aggressors with any real advantage.

[Sources: Bruce Catton, 'Mr. Lincoln's Army' & 'Glory Road'; James McPherson, 'Battle Cry of Freedom']