It’s unacceptable that what to wear at work is still an issue in 2018. Tons of women choose not to work heels and are quite successful in their jobs. It’s silly to suggest that putting on heels would help you close more clients swiftly. Your performance triumphs how you look. Times are changing now. Think: Mark Zuckerberg in a grey hoodie.
Your boss needs to reassess what part of workplace dress codes are acceptable in this day and age. And meanwhile, you might point out to him that he is enforcing a sexist double standard of expecting women to wear heels to work.