Several items come to mind. Most puddings are made with corn, or tapioca starches. Custards are thickened with eggs and contain no flour. There are also shaved ice deserts, Itallian ices, ice crea products, gelatine deserts. flan, and a host of others. And by using dairy products and starches, you can make a host of deserts ranging from extravagant parfaits, to a simple bowl of jello. You can add fruits to gelatin, or serve fruits with fine cheese, or serve poached fruits or candied fruits, etc. And don't forget shakes, sorbet, sherbert, hot-mulled-apple cider, baked apples with caramel, strawberries, either on there own, or diped in chocolate or whipped cream. Then there are a whole bunch of fruit salads, and desserts made with creamed cheese (who says cheese cake has to have a crust? I've succesfully baked one without any kind of crust whatsoever. I just lined the springform pan with parchment paper and served the baked custard without the crust). And don't forget yogurt and cottage cheese as a base for poached pears with chocolate sauce.
The list of deserts made without flour products is staggering. Just get the cakes, pastries, quickbreads, and pies out of your head and start thinking other things. You will have no trouble. And the other desserts can be as simple or extravagant as you want to make them.
Seeeeeya; Goodweed of the North