How about this for a possibility? At full thrust the aircraft was not limited by FLL OEI and therefore a theoretical range of decision speeds was available at the actual TOM. Using made-up numbers assume VEF = 138KT V1 = 140KT and the range of V1s exists from 130KT to 150KT. Now assume a VMCG at 143KT, VEF thus calculated is not greater than or equal to VMCG but a procedure would allow VEF and V1 to be raised within the range of speeds available so that VEF = 143KT, V1 say 145KT. Now you have a legal take-off at full thrust.
A FLEX take-off has the effect of making the take-off limiting at the lower thrust. If there were no other constraints such as climb limit, 2nd sector etc, this would mean the take-off becomes FLL at 140KT-ish, but it doesn't meet the VMCG criteria with a VMCG (calculated at full thrust as observed above) of 143KT.