All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The Sunnah in regard to how women walk in the streets is that they should walk with calmness and composure, not with quick steps, because Ramal (walking quickly) is not prescribed for women in Hajj in places where Ramal is legislated, such as for Tawaaf Al-Qudoom (the Tawaaf upon arriving in Makkah) and the Sa’y (going back and forth) between Mount Safa and Mount Marwah.
Ash-Shaafi’i said his book Al-Umm, “Women do not have to walk quickly in the Sacred House [i.e. al-Masjid al-Haraam when performing Tawaaf – circumambulation around the Ka’bah) nor between Safa and Marwah; rather, they should walk with their normal pace.”
Also, women should not crowd with men, so they should not walk in the middle of the street. It was reported by Abu Daawood from Abu Usyad Al-Ansaari, may Allah be pleased with him, that he heard the Prophet while he was coming outside the mosque and men mixed with the women in the street, say to the women, “Draw back, for you (women) must not walk in the middle of the road; keep to the sides of the road.” Then the women walked so close to the walls that their garments rubbed against them.
Moreover, women should not walk in a manner that attracts attention; Allah forbade the believing women from stamping their feet so that they would not attract the attention of men. Allah says (what means): {And let them not stamp their feet to make known what they conceal of their adornment.} [Quran 24:31]
At-Taahir ibn ‘Aashoor said in At-Tahreer wat-Tanweer, “This requires forbidding anything that could remind men of the distraction of women and arouse them by anything that he hears or sees from their adornment or movement, such as them walking in an attractive, swaying manner or singing…”
Allah knows best.