Lenny, you may need to add SoftmaxLayer.
So something like this will work:
testNet =
NetChain[{LinearLayer[10], SoftmaxLayer[]},
"Input" -> NetEncoder[{"Image", {28, 28}, "Grayscale"}],
"Output" -> NetDecoder[{"Class", Range[0, 9]}]]
I've tried this. The accuracy was 0.7621 because of a simple neural network.
trainedNet =
NetTrain[testNet, trainingData, BatchSize -> 1000,
MaxTrainingRounds -> 1];
cm = ClassifierMeasurements[trainedNet, testData];
cm["Accuracy"]