It really depends on what you want your trainable parameters to be. For a model such as

a * Input1 * Input 2 + b * Input3 + c

you can use this network

FunctionLayer[
 Function[
  NetArray[]*#Input1*#Input2 + NetArray[]*#Input3 + NetArray[]]]

If, let's say, the input are 5-d arrays, the fully specified net will be

d = 5;
net = NetInitialize@FunctionLayer[Function[
    NetArray["Dimensions" -> d]*#Input1*#Input2 +
     NetArray["Dimensions" -> d]*#Input3 +
     NetArray["Dimensions" -> d]],
   "Input1" -> d, "Input2" -> d, "Input3" -> d]