Magnetic nanoparticles are an important asset in many biomedical applications ranging from the local heating of tumours to targeted drug delivery towards diseased sites. Recently, magnetic nanoflowers showed a remarkable heating performance in hyperthermia experiments thanks to their complex structure leading to a broad range of magnetic dynamics. To grasp their full potential and to better understand the origin of this unexpected heating performance, we propose the use of Kaczmarz' algorithm in interpreting magnetic characterisation measurements. It has the advantage that no assumptions need to be made on the particle size distribution, contrasting current magnetic interpretation methods that often assume a lognormal size distribution. Both approaches are compared on DC magnetometry, magnetorelaxometry and AC susceptibility characterisation measurements of the nanoflowers. We report that the lognormal distribution parameters vary significantly between data sets, whereas Kaczmarz' approach achieves a consistent and accurate characterisation for all measurement sets. Additionally, we introduce a methodology to use Kaczmarz' approach on distinct measurement data sets simultaneously. It has the advantage that the strengths of the individual characterisation techniques are combined and their weaknesses reduced, further improving characterisation accuracy. Our findings are important for biomedical applications as Kaczmarz' algorithm allows to pinpoint multiple, smaller peaks in the nanostructure's size distribution compared to the monomodal lognormal distribution. The smaller peaks permit to fine-tune biomedical applications with respect to these peaks to boost heating or to reduce blurring effects in images. Furthermore, the Kaczmarz algorithm allows for a standardised data analysis for a broad range of magnetic nanoparticle samples. Thus, our approach can improve the safety and efficiency of biomedical applications of magnetic nanoparticles, paving the way towards their clinical use.