Guess there is nobody here in dentistry huh?
Flossing isn't just to remove food from between teeth; it is essentially the only way we can effectively clean in between our teeth. Simple as that.
Tooth brush bristles can't clean the surfaces between our teeth. Overtime, the bacteria that live in our mouths develop into colonies that form a hard layer. This can't be removed without a dentist and very often leads to cavities ('carious lesions' to be precise). This can be both painful and expensive.
Brushing (on surfaces) and flossing (between teeth) physically destroys the bacterial colonies before they develop into a hard layer.
So yes, while flossing does remove food from between teeth it does a lot more; it helps prevent a significant cause of dental visits.
As for timing, the ADA says it doesn't matter. Just brush every surface of every tooth gently.
Mouthwash is helpful as it kills many of the bacteria that you have just dislodged from resettling.
It's work, but it's worth it; chronic dental infections are associated with many systemic problems.
Hope this helps.