Generally speaking the best friendships between exes occurs after there has been a large gap of time since they broke up. They've both moved on to being involved or married to other people and bump into one another.
They exchange email addresses and drop each other a line from time to time. Even with that in most scenarios their contact is often done without their current mate's knowledge. One of the main problems with the exes can be friends arrangement is oftentimes their current mates/spouses don't approve of it. The only exception is if they had children together. Even then they want them having limited contact.
In fact this is one of the reasons why many best friendships between "platonic male and female friends" tend to drift apart.
Someone falls in love with a person who objects to their friendship. Most people will choose love over a "platonic friendship" with the opposite sex.
Having said that it is probably unrealistic to expect to go from "red hot lovers" to a brother/sister friendship. Rarely is their instance where both people want to end a relationship at the same time.
The person who initiated the breakup offers friendship as a "consolation prize" as not to feel like the "bad guy" and the hurt person accepts it with the hope that one day they might reconcile.
It's not a "real platonic friendship".