Perhaps the GAP function IsomorphismFpAlgebra
can be used to obtain what you want?
I tested the following small example:
p := 3;
K := GF(p);
G := CyclicGroup(p);
KG := GroupRing(K, G);
A := Image(IsomorphismFpAlgebra(KG));
F := FreeAlgebraOfFpAlgebra(A);
R := RelatorsOfFpAlgebra(A);