Flexible work is increasingly pursued as a means of achieving work-life balance, particularly as growing caregiving responsibilities for children and aging family members shape workers’ lives. Yet most HCI research has examined flexibility primarily through productivity and organizational perspectives, with less attention to how it intersects with workers’ personal and family responsibilities. To address this gap, we conducted a qualitative study with 20 workers in Singapore engaging in flexible arrangements to manage paid work and care responsibilities. Using an asset-based lens, we show that flexibility is not a static benefit but a continual practice of rhythm-making. Participants maintained rhythms by drawing on temporal and spatial assets, negotiated them through relational and institutional dynamics, and sustained them through intrapersonal assets such as self-care and positive reframing. Our study reframes blurred boundaries as resources rather than disruptions and offers design implications for technologies that support flexible workers’ everyday rhythm-making practices.