Someone told me that it's assur (or inappropriate? either way...) to break any fast with meat. They didn't have a source, and I wasn't familiar with one, so I looked into it. I only found one relevant halacha.
Hilchos Tisha Baav Simman 558
בְּתִשְׁעָה בְּאָב לְעֵת עֶרֶב הִצִּיתוּ אֵשׁ בַּהֵיכָל וְנִשְׂרַף עַד שְׁקִיעַת הַחַמָּה בְּיוֹם עֲשִׂירִי, וּמִפְּנֵי כָּךְ מִנְהָג כָּשֵׁר שֶׁלֹּא לֶאֱכֹל בָּשָׂר וְשֶׁלֹּא לִשְׁתּוֹת יַיִן בְּלֵיל עֲשִׂירִי וְיוֹם עֲשִׂירִי. הַגָּה: וְיֵשׁ מַחְמִירִין עַד חֲצוֹת הַיּוֹם וְלֹא יוֹתֵר (הַגָּהוֹת מַיְמוֹנִי); אִם חָל תִּשְׁעָה בְּאָב בְּשַׁבָּת וְנִדְחָה לְיוֹם א', מֻתָּר לֶאֱכֹל בָּשָׂר וְיַיִן יוֹם ב', אֲבָל בַּלַּיְלָה אָסוּר מִפְּנֵי אֲבֵלוּת שֶׁל יוֹם (מַהֲרִי''ל).
In the evening of the 9th of Av, a flame engulfed the Heichal and burned until sunset of the 10th. Therefore the custom is to refrain from meat and wine on the night of the 10th and the day. Rema: some are strict until noon and no later. If Tisha Baav falls on Shabbos and is pushed off until Sunday, it is permissible to ear meat and drink wine the next day, but not the night after due to the mourning of the day.
You can infer from this that only after Tisha Baav a person shouldn't break their fast with meat, unlike other fasts. However you could argue that in general you shouldn't and after Tisha Baav is more strict since you can't have meat even after you break your fast.
However the Rema's last halacha is telling. If Tisha Baav is pushed off to the next day, really there's no problem eating meat afterwards, if not for the problem of the mourning of the day.
The Mishnah Berurah Seif kattan 5 infers:
ה) מפני אבילות של יום - משמע דרק בזה מפני אבילותו של ט"ב מחמרינן גם בלילה שאחריו דהוא כמו בין המצרים דיש אנשים שמחמירין על עצמן מבשר ויין אבל בשארי תעניתים אין להחמיר בזה:
Because of the mourning. Sounds like it's only because of the mourning of Tisha Baav are we strict not to eat meat even the night after, since it's like the 3 weeks that there are those who are strict not to eat meat. However regarding other fasts a person shouldn't be strict.
However, the MB is discussing eat meat that night, not with what to break your fast.
Is there anyone who actually prohibits breaking a fast with meat?