My reason for asking is because I want to know if i should some how "flush" out my router
If your router is queuing packets, and it's unlikely that it is, its only going to be for a fraction of a second. And even if it was queuing packets, they're not going to come back into your private network. A router will only forward a packet in the direction of it's destination address.
You don't have much to worry about when it comes to packets stored. They all have a field in the header called Time-To-Live. This sets a maximum amount of time for the packet to be on the network before it is eventually dropped.
The TTL field is merely a hop count to prevent a packet from circling around forever in the case of a routing loop. When a packet crosses a router, it's TTL field is decremented by one. It is in no way a measure of time.