Can you wear foot orthotics in ballet flats?
Short answer: no.
Ballet flats are a style of footwear for everyday use based on the ballet shoe used by dancers, so by design it is minimalist and so does not have much room in the shoe for anything, let alone a foot orthotic.
What should you do if you need foot orthotics and like to wear ballet flats?
The obvious answer is to stop wearing those types of shoes! Get into footwear that you can wear foot orthotics in and help you get over the problem that the foot orthotics were prescribed for. This may only be needed as a short to medium term change in your footwear choices. As your problem improves, you may be able to start going back to wearing your ballet flats style of shoe for limited periods of time initially and gradually increasing the use of them over time. For some cases, this may never be possible and will depend on the nature of the problem that you have and he nature of that. No one’s problems are the same.
You can get adhesive pads, some made of silicone gel to create an arch support in ballet flats that are probably not going to be as effective as properly prescribed foot orthotics, but they will be better than nothing if you have to wear this type of footwear.
Another option, is that depending on what is causing the problem that you might need foot orthotics for, is that you may have other options instead of foot orthotics. There are some foot types and biomechanical problems that respond well to exercise. There is no blanket advice here and everyone is going to be different. The best advice is use your commonsense regarding the arch support in ballet flats and talk to your podiatrist about the options and which is probably the best course of action for you to follow.