Only MyFitnessPal Premium currently supports timestamps for logged foods on iOS and Android. This option can be turned on or off within the Diary Settings in app.
Free users can still customize their meal names to include a time range. For example, you can change your meal names to:
Breakfast 7am-10am
Snack 10am-12pm
Lunch 12pm-3pm
Snack 3pm-5pm
Dinner 5pm-9pm
Snack 9pm-7am
Please see this article for more information on changing your meal names.