This isn’t something a node can do on its own. To compute an estimate of the propagation time, multiple active monitoring nodes (running modified/custom software) need to be deployed to track how long it takes for a transaction sent from a given source to reach all of them.
This is the approach followed by KIT@DSN as far as I can tell. They do collect and report multiple stats on their website, including the propagation time of transactions.
According to the most recent data, a transaction takes about ~7 seconds to reach 50% of the network, and about ~17 seconds to reach 90%. Notice that this doesn’t mean it will take that long to reach miners. Miners are likely to be better connected than regular nodes, so I’d expect them to receive most transactions closer to the 7-second mark.
