An IC engine needs air, fuel, spark, and exhaust to run. Assuming you have an automatic, needs a functional torque converter to accelerate.
Easy stuff first.
Engine runs smooth with smooth idle?
Warmed engine, parking brake on, service (foot) brake depressed, floor accelerator and read rpms. This is your "stall speed" and should be about 2000 rpm. Higher is ok. If in the 1500 range, bad torque converter. You need about 2000 rpm for the engine to reach a speed that develops enough launch torque. Too low rpm and the torque is not there.
Assuming that's ok.
Confirm you have good air entry, no dirty air filter, or blockages.
You seem to have confirmed good fuel flow. A dirty fuel filter or poor fuel pump will "run out" of fuel during hard acceleration...that is you will sputter after fuel throttle shift into 2nd, etc. I have seen where stuff was thrown in the gas tank and slowly disintegrated, periodically blocking the inlet screen and fuel filter.
Confirm that exhaust flow is good. Have someone rev engine while you feel exhaust flow. Should be strong flow (and not burn your eyes from rich unburned fuel). I have seen dual walled exhaust pipe that internally separated and blocked flow.
Now the hard stuff.
Stretched timing chain or worn out camshaft. What is the idle intake manifold vacuum? How does the vacuum behave on sudden throttle opening? Vacuum gauges are cheap or use the bluetooth OBD II dongle and the Torqe app. Search the internet for "engine vacuum test" to learn about how problems affect the vacuum.