The internal dynamics of multiple stellar populations in Globular Clusters (GCs) provides unique constraints on the physical processes responsible for their formation. Specifically, the present-day kinematics of cluster stars, such as rotation and velocity dispersion, seems to be related to the initial configuration of the system. In recent work (Milone et al. 2018), we analyzed for the first time the kinematics of the different stellar populations in NGC 0104 (47 Tucanae) over a large field of view, exploiting the Gaia Data Release 2 proper motions combined with multi-band ground-based photometry. In this paper, based on the work by Cordoni et al. (2019), we extend this analysis to six GCs, namely NGC 0288, NGC 5904 (M 5), NGC 6121 (M 4), NGC 6752, NGC 6838 (M 71) and further explore NGC 0104. Among the analyzed clusters only NGC 0104 and NGC 5904 show significant rotation on the plane of the sky. Interestingly, multiple stellar populations in NGC 5904 exhibit different rotation curves.