range[x_, r_] := Module[{interval},
   i = IntegerPart[(x - 1)/r]; interval = Range[r i + 1, r i + r]];
qflat[x_, r_] :=
  AnyTrue[Subsets[range[#, r] & /@ x, {2}],
   IntersectingQ[#[[1]], #[[2]]] &];
flatQ[par_, r_] := AnyTrue[par, qflat[#, r] &];
pickflat[par_, r_] :=
  Select[Transpose[{par, flatQ[#, r] & /@ par}], #[[2]] ==
      False &][[All, 1]];
Needs["Combinatorica`"];
par = SetPartitions[Range[1, 12]];
SetPartitions[Range[1, 12]] // AbsoluteTiming // First
pickflat[par, 4] // AbsoluteTiming // First