Hi
@grannybaker
It sounds to me that you have overbeaten your mixture with the hand whisk, causing too much gluten to form and thus resulting in a dense cake.
When you make the flan by hand, I'm assuming you slowly fold the flour into the cake until the mixture is combined, whereas when you've used the hand mixture, I think you may have slightly overdone it.
I use a hand mixer for a lot of my bakes that way I can 'feel' that batter but when I add flour to my mixtures after the creaming method I only beat the mixture in after I've folded the flour with a spatula and then I hand whisk for about 10-20 seconds so not to over beat the mixture.
The way I test to see if the mixture has combined is to taste it, if it tastes a touch floury I whisk for a few more seconds if it tastes okay I'm good.
If you get an excellent flan doing it manually then I would stick with the method that gives you the best results.
Either that or try it again, but whisk slowly and for less time.