If we treat the early shells of the 1370s as something that could have happened ITTL (or about to), it could be as simple as a bitumin-cloth ceramic shell.The best use of it I can think of is as an explosive in a Howitzer-type cannon where the goal is not to plow through ranks of infantry at long range but lob an AoE projectile over the ranks or walls or wagons a shorter distance to deliver an explosive charge. Sort of like the houfnice of the Hussite Wars I suppose.
Alternatively clay grenades with lit fuses or otherwise (if Greek fire ignited by contact with oxygen then fuses would not be necessary) could be useful for light cavalry raiding groups to charge into a camp or village and lob them at something to shatter and ignite before turning around and retreating. They could potentially also be useful as something to drop on enemies from the tops of walls or other fortifications. They would also be fantastic given to melee troops to shatter pike formations or other massed infantry if they could get close enough. It could give the Romans grenadier type units long before they were invented IOTL.
And if you want to go absolutely crazy you could combine the two and have clay or iron grenades filled with Greek fire launched from a handcannon on horseback into lines of musketmen or other massed infantry.
I mean (1) A damn shell. . Start making that standard use in Roman artillery and you've got an edge for sure. But take the principle of the shell and the bitumen cloth starts it burning from firing, and since you're not too fussed about whether your Greek Fire is dispersed on impact with the ground, or mid-air, as long as it isn't IN THE CANNON - and you've got a terrifying, and simple, method of deploying it.
.... I look forward to a Roman Artillery College.
Plus, a slightly more reckless use would be in hand grenades given to light cavalry. I don't know what the typical burn time of the stuff is meant to be, but light cavalry sent out to deny a flank by dropping Greek fire hand grenades behind them with a short fuse? (Or even dropping them behind them when pursued?) I wouldn't be chasing Roman cavalry after that. (Poor Horses).