OK so here are my questions. Can I run a subpanel from a subpanel?
Generally speaking, yes. You could put a million subpanels in series, and by itself that wouldn't be a code violation.
Subpanel (A)(existing subpanel) has a three wire feed from the main ran underground through metal conduit and ground and neutrals are connected, I am guessing because this met code not long ago soI guess my question is do I need to run a 4th wire from main panel to subpanel(A) before running 4 service entrance wires to subpanel (B)(new subpanel) or use the conduit as a ground and seperate ground and neutral bus bars
The metal conduit can act as the equipment ground so a 4th wire is not required. (But you may want to test the resistance to make sure it hasn't rusted away, or actually transitions to PVC somewhere, or something like that.)
Yes, you most likely need to separate the grounds and neutrals. But if it turns out that the metal conduit is not continuous and won't act as a ground, then read the Exception to 250.32(B) very carefully.
Also subpanel(B) will be about 250 ft away will that cause voltage drop?
Voltage drop is a function of current as well. One would need to know the projected load on both panels and the size of the wires feeding the existing panel to address the question properly. But yes, at 250ft the effect should be considered.