flowmap.blue offers a relatively easy way to create flow maps in a web browser. It's also possible to create the maps from data in a google sheet. https://flowmap.blue/in-browser
Tom Chadwin describes how he created pseudo-3d arched flow lines using QGIS https://medium.com/@tomchadwin/mapping-emotion-fighting-school-closures-with-qgis-28842661bf14
"Design principles for origin-destination flow maps", an article by Bernhard Jenny, et al. discusses all the things you'll want to think about for the cartography of a flow map. http://www.cartography.oregonstate.edu/pdf/2017_Jenny_etal_DesignPrinciplesForODFlowMaps.pdf
"Untangling origin-destination flows in geographic information systems", an article by Anita Graser, et al. presents a technique for clustering edges (flow lines) to bring some order to a cluttered flow map. https://journals.sagepub.com/doi/full/10.1177/1473871617738122
Anita Graser's QGIS implementation of edge bundling is available at: https://github.com/dts-ait/qgis-edge-bundling