There are various Minhagim when to begin not eating meat before Tisha B'Av. Some say we stop eating meat as far back as 17 Tammuz. Some don't even meat on Shabbos during the nine days. The minhag of Ashkenazim is not to eat meat starting from Rosh Chodesh Av. What about Seudas Rosh Chodesh itself when there is a minhag to eat a fleishig seuda?
The Maharil and the Seder HaYom (from the times of the Arizal) both say that we do not eat meat even for the Seudas Rosh Chodesh. The reason, says the Seder HaYom is that we eat meat on Rosh Chodesh because, as the first day of the new month, it is a day of Simcha. Not so Rosh Chodesh Av which is a month of Puranus, troubles. Also it is the day that Aharon HaKohen was niftar. This is also the opinion of the Arizal in Shaar HaKavanos.
However the Shiyarei Knesess HeGedola writes that the minhag in Turkey, at the time, was to eat meat and drink wine during the Rosh Chodesh Seudah, even in Av. This is also the opinion of the Chida. The Toras Chaim says that if it is your minhag to consistently eat a celebratory seudah with meat and wine each Rosh Chodesh, you should do so on Rosh Chodesh Av as well. The Darkei Chaim V'Shalom takes this a step further and says you should only eat meat if you are noheg like the Talmidei Baal Shem Tov and make a public seudah every Rosh Chodesh. (See Minhag Yisroel Torah 551:6)