There are a multitude of situations where you can be denied your dexterity bonus to AC. Technically you are only "flat footed" in the first round of combat but many people use the term "flat footed" to refer to all of the other cases too.
So the most usual case is during a surprise round or the first few rounds of combat where you have not yet had a turn:
Unaware Combatants: Combatants who are unaware at the start of battle don't get to act in the surprise round. Unaware combatants are flat-footed because they have not acted yet, so they lose any Dexterity bonus to AC.
Note that Unaware Combatants refers to people completely unaware of a fight happening, it does not mean being unaware of specific targets in the fight. The rules for that are covered under stealth, invisibility and concealment.
There are in fact a large number of other situations which also deny you your dexterity bonus. A list can be found here: In what situations would a target be denied a Dex bonus to AC?.
Looking through this list you can see that none of them cover "creature just appeared next to me" so unless the summons were invisible or concealed in some way you would not be flat footed.
To give a more flavorful and less rules based answer: You would see and hear the summons appearing and hence be able to respond to them and defend yourself even if it is not your turn yet.