There is no Muslim pride flag. Why not? (Disclaimer: From this point onwards, the answer is mainly opinion-based). Potentially the reason may be that the Prophet ﷺ did not have a specific flag in his lifetime.
Prior to the Hijra, the Prophet ﷺ and his companions were undoubtedly a minority group in the society of Mecca. During this period of 13 years of torture, oppression, and isolation, the Prophet ﷺ gave his companions one advice: patience, as in the story of the torture of Khabbāb bin Al-Aratt, who was enslaved at a young age, until finally bought by Umm Anmār in Mecca. He used to accompany the Prophet ﷺ prior to the first revelation. Then he became the sixth person to embrace Islam. Umm Anmār used to torture him with fire. Khabbāb and other companions complained to the Prophet ﷺ:
عَنْ خَبَّابِ بْنِ الأَرَتِّ قَالَ شَكَوْنَا إِلَى رَسُولِ اللَّهِ صلى الله عليه وسلم وَهْوَ مُتَوَسِّدٌ بُرْدَةً لَهُ فِي ظِلِّ الْكَعْبَةِ فَقُلْنَا أَلاَ تَسْتَنْصِرُ لَنَا أَلاَ تَدْعُو لَنَا. فَقَالَ: قَدْ كَانَ مَنْ قَبْلَكُمْ يُؤْخَذُ الرَّجُلُ فَيُحْفَرُ لَهُ فِي الأَرْضِ فَيُجْعَلُ فِيهَا، فَيُجَاءُ بِالْمِنْشَارِ فَيُوضَعُ عَلَى رَأْسِهِ فَيُجْعَلُ نِصْفَيْنِ، وَيُمَشَّطُ بِأَمْشَاطِ الْحَدِيدِ مَا دُونَ لَحْمِهِ وَعَظْمِهِ، فَمَا يَصُدُّهُ ذَلِكَ عَنْ دِينِهِ، وَاللَّهِ لَيَتِمَّنَّ هَذَا الأَمْرُ، حَتَّى يَسِيرَ الرَّاكِبُ مِنْ صَنْعَاءَ إِلَى حَضْرَمَوْتَ لاَ يَخَافُ إِلاَّ اللَّهَ وَالذِّئْبَ عَلَى غَنَمِهِ، وَلَكِنَّكُمْ تَسْتَعْجِلُونَ
Narrated Khabbab bin Al-Aratt: We complained to Allah's Messenger (ﷺ) (about our state) while he was leaning against his sheet cloak in the shade of the Ka'ba. We said, "Will you ask Allah to help us? Will you invoke Allah for us?" He said, "Among those who were before you a (believer) used to be seized and, a pit used to be dug for him and then he used to be placed in it. Then a saw used to be brought and put on his head which would be split into two halves. His flesh might be combed with iron combs and removed from his bones, yet, all that did not cause him to revert from his religion. By Allah! This religion (Islam) will be completed (and triumph) till a rider (traveler) goes from San'a' (the capital of Yemen) to Hadramout fearing nobody except Allah and the wolf lest it should trouble his sheep, but you are impatient."
— Sahih al-Bukhari 6943
After Hijra, the Prophet ﷺ adopted multiple flags with no particular consistency, potentially on purpose, but mainly during battles.
In Fath al-Bari, Ibn Hajar said the Prophet ﷺ had two flags: a white one and a black one. This is based on a number of hadiths, e.g., Ibn 'Abbas said his flag was black, and his standard was white (Jami' at-Tirmidhi 1681). Al-Barā' ibn 'Azib said it was black and square, made of a woolen rug (Sunan Abi Dawud 2591). There are other hadiths to the same effect, with some mentioning the flag used on one occasion being red (Ibn Abi 'Āsim), or yellow (Simak ibn Harb).
When asked about the different colors, Badr al-Dīn al-'Ayni in his book 'Umdat al-Qāri (Arabic: عمدة القاري شرح صحيح البخاري) said that it changed over time.