Iron oxide nanoflowers (IONF) are densely packed multi-core aggregates known for their high saturation magnetization and initial susceptibility, as well as low remanence and coercive field. This study reports on how the local magnetic texture originating at the crystalline correlations among the cores determines the special magnetic properties of individual IONF over a wide size range from 40 to 400 nm. Regardless of this significant size variation in the aggregates, all samples exhibit a consistent crystalline correlation that extends well beyond the IONF cores. Furthermore, a nearly zero remnant magnetization, together with the presence of a persistently blocked state, and almost temperature-independent field-cooled magnetization, support the existence of a 3D magnetic texture throughout the IONF. This is confirmed by magnetic transmission X-ray microscopy images of tens of individual IONF, showing, in all cases, a nearly demagnetized state caused by the vorticity of the magnetic texture. Micromagnetic simulations agree well with these experimental findings, showing that the interplay between the inter-core direct exchange coupling and the demagnetizing field is responsible for the highly vortex-like spin configuration that stabilizes at low magnetic fields and appears to have partial topological protection. Overall, this comprehensive study provides valuable insights into the impact of crystalline texture on the magnetic properties of IONF over a wide size range, offering a deeper understanding of their potential applications in fields such as biomedicine and water remediation.