"Phlogiston" was removed from any list of "elements" in the late 1700s (around 1790) when Lavoisier demonstrated the existence of an element called Oxygen, and how "fire" was the result of the rapid combination of oxygen with other material.
Since the first attempts at creating a periodic table happened after 1850, then we know that "fire" (phlogiston) was never included in the periodic table, having been proven non-existent more than 50 years before that.
Since "fire" is the result of the rapid oxidization of "stuff", then look for elements that have properties close to oxygen, when it comes to valence and electronegativity: they include Oxygen itself (of course), chlorine, fluorine, and so on.
Therefore, the answer to your question would be: In the top-right corner of the periodic table (if you exclude the noble gases in the last column).
To oxidize material with a reaction that we describe as "fire", the oxidizer must (normally) be available in gas form, so that the burning material can evaporate molecules that violently react with the oxidizer in a way that releases heat, itself sufficient to sustain the rapid evaporation of "burning material".
There; aren't you sorry you asked?