The oldest philatelic magazine in the world, still alive, is the American Philatelist. Its first issue was released in January 1887. A few months later, in November, the second oldest surviving to date, L’Écho de la timbrologie was introduced to the philatelic public.
A surprising third is the Schweizer Briefmarken Zeitung (SBZ), the official magazine of the Swiss Philatelic Federation, which was first issued in 1888! For the last twenty years or so the SBZ lies in the experienced hands of its Editor-in-chief, Hans Schwartz AEP, AIJP, who is currently also the FEPA Treasurer.
In order to get acquainted with SBZ, go to https://www.vsphv.ch/schweizer-briefmarken-zeitung. You will find there the Table of Contents and a sample article of almost each number as far back as 2014.