Is there a way to make this work with unsweetened coconut flakes?

Jensiegelnyc - yes you can.
I'm saying from both past baking exoerience and checking other recipes for custardy macaroons.
You don't even have to, but might want to, add a little bit of fine granulated sugar to match the sweetness you would have had from sweetened dried coconut.
Happy almost Passover!