How do you straighten a flexible Hammer toe without surgery?

You can't. There are silcone pads on the market that sit under the toe and are used to move it into a straigher position over time but they are not successful for most foot ailments and are not successful for hammer toe. If the toe is not painful and one is considering surgery for cosmetic reasons, the best option is to leave it. If the toe is painful or one decides the cosmetic reasons are sufficient, surgery is the only option. Importantly, one needs to be aware of why the hammer toe developed in the first place. Meaning, if surgery is completed, the reasons for the development of toe also need to be address. Ill fitting footwear e.g. narrow shoes or squeezing feet into the trendy and stylish heels are a common source of hammer toe, are a common cause. So if one insists on maintaining improper foot care, the hammer toe can redevelop. Genetic factors also come into play and whilst there is nothing one can do about these, one must take steps to limit hammer toes developing, such as not wearing narrow shoes.