There are three subtle problems with how you define your function ff. The first is that you collect the arguments in a list {c1...}. Consider the two following functions:
f[x_, y_, z_] := x^2 + y z;
g[{x_, y_, z_}] := x^2 + y z;
The two functions achieve the same goal, but the input is packaged in two different ways. The function f is a function of THREE variables, one in each slot. The function g is a function of ONE vector variable. The mechanism of Derivative relies on the counting of slots, so that it only applies to f, not to g. Try to calculate the derivative with respect to y:
Derivative[0, 1, 0][f][x, y, z]
Derivative[0, 1, 0][g][{x, y, z}]
The second problem is that you define ff only for NUMERIC values of the variables ff[{c1_Real, c2_Real... This makes it impossible to calculate the derivatives, because calculating a derivative involves the function calculated on a SYMBOLIC input.
The third problem is that your ff depends on 13 variables, while your derivative operator nder[n, 12, ff] assumes 12 variables.
The following code runs without errors:
sig = 1/10; teq = 1;
cout0 = Table[If[i <= 4, 1, 1/16], {i, 1, 6}];
nder[n_, m_, f_] := (Derivative @@ UnitVector[m, n])[f];
ccvar = Table[cc[i][t], {i, 6}];
ff[c1_, c2_, c3_, c4_, alpha11_, alpha21_, alpha31_, alpha41_,
alpha12_, alpha22_, alpha32_, alpha42_, alpha13_] = 1;
eqnlist = Flatten[Table[{Derivative[1][cc[n]][t] == sig*
nder[n, 13, ff][Sequence @@ Flatten[{ccvar, ccvar}]],
cc[n][0] == cout0[[n]]},
{n, 6}]];
solDEsuper = NDSolve[eqnlist, ccvar,
{t, 0, teq}]
