This paper studies the links between scaling properties of river flow time series by comparing the results of three techniques applied to an extended data set of 34 French discharge gauging stations. The three approaches used are based on different mathematical tools and hypotheses: (1) shape analysis of flood hydrographs; (2) a multifractal framework through spectral and moment analyses, and (3) flood frequency analysis through the fitting of flood duration frequency curves (QdF). The general aim is to test the hypothesis of scaling invariance of river flow and the shape invariance of the hydrographs, in order to investigate the link between scaling properties and flow dynamics. In particular, the coherence between different approaches widely used in the literature to describe these characteristics is evaluated through the estimation of parameters defining the range of time-scales on which the scaling properties are valid. The results show that most of these timescale parameters are linked to the flow dynamics and suggest that the approaches applied are interrelated.