The Koinobori Festival runs from July 25th 05:00 LNST to July 31st 23:59 LNST. Stylists will play regular journey stages to earn Carp Streamers throughout the duration of the event. The Koinobori Kimono will be obtained by collecting Carp Streamers.
The general recommendation is to play the game as usual, keep farming items for your target suits, and use any extra stamina to play Maiden stages like 2-S2, 3-S1, 7-7, and 8-5, as these stages drop good items for decomposing for Rebirth materials, and will help maximize your participation in the event.
Good luck, and happy styling!