Flanking applies to attackers
The flanking rules say:
To flank a foe, you and your ally must be on opposite sides of the creature. A line drawn between the center of your space and the center of your ally's space must pass through opposite sides or opposite corners of the foe's space
That is, for you, the attacker under consideration, it matters if you have an ally on the other side. The creature in the middle does not gain some kind of "flanked" status flag if it is flanked by some other creatures. You check for each creature around it if the flanking conditions are fulfilled.
In your example, there is no ally onyou can't draw a line from the opposite sidecenter of player 3, so and cross both opposite sides of the enemy square with any other ally. Thus player 3 does not get the advantage of flanking.
There is even an image in the rules that explains this situation:
Here Merisel is your player 3, and Valeros and Kyra are your players 1 and 2. They flank the creature, Merisel does not.