Screen time? For Star Wars only two are ever seen on screen at a time and only for one brief shot.
For The Empire Strikes Back there are apparently four Star Destroyers accounted for which are a part of Darth Vader’s personal “Death Squadron” that are clearly mentioned in the storyline. But there is one brief shot in the film where six Star Destroyers are clearly seen in formation.
In the case of Return of the Jedi, there are six specific Star Destroyers accounted for as being present at the “Battle of Endor”, but looking at a screenshot of the final battle reveals there are many, many, many, many more than just six Star Destroyers involved in that battle.
So the largest number of Star Destroyers shown on screen at one time in the original trilogy is undeniably the 24+ seen in the final, climactic space battle at the end of Return of the Jedi. But since not all of the Star Destroyers are accounted for in the story itself, only about six specific ships can be actually be identified with a name.
Here’s a breakdown of the Star Destroyers presented on screen in Star Wars (1977), The Empire Strikes Back (1980) and Return of the Jedi (1983):
Star Wars (1977): Two Star Destroyers Seen On Screen
While it’s clear that the first Star Wars film showed the least amount of Star Destroyers, I think it’s worth mentioning which Star Destroyers were present in that film since the Devastator appears in all three original trilogy films:
These two Star Destroyers can both be seen on the screen pursuing the Millennium Falcon which had just escaped from Mos Eisley spaceport in this screenshot:
The Empire Strikes Back (1980): Six Star Destroyers Seen On Screen
According to the Wookieepedia, Darth Vader’s personal “Death Squadron” in this film consisted of four Star Destroyers; one Executor-class Star Dreadnought (Super Star Destroyer) and three Imperial-class Star Destroyers:
That said, one shot clearly shows six ships appearing in the “reveal” scene with Darth Vader near the beginning of the film:
Return of the Jedi (1983): Way Too Many Star Destroyers to Count On Screen
Not as clear cut as The Empire Strikes Back since what is accounted for in the story details and what is shown on screen is exponentially larger.
According to the Wookieepedia entry on the “Battle of Endor” as presented in Return of the Jedi, it involved one Executor-class Star Dreadnought (Super Star Destroyer) and five Imperial-class Star Destroyers:
Seems simple enough superficially, but here is a screenshot of the scene where the Rebel fleet breaks off the attack on Death Star II and is caught in “a trap” where they have to face off against seemingly the whole Imperial fleet:
I casually counted about 24 ships that seem to be Star Destroyers but I give up… There’s too many of them!
But seriously, the most amount of Star Destroyers—and pretty much anything that flies in space—in the whole original Star Wars trilogy can be seen in that final space battle at the end of Return of the Jedi.