Is there anyway I can save the flow arrows as a separate layer or be converted into graphics?
Did you check Save To Layer File—Help | ArcGIS for Desktop (You could also right-click the layer on TOC > Save as layer file). If you want to preserve the symbology and other layer properties, this is the best option.
You could also check Converting features into graphics—Help | ArcGIS for Desktop , as desired.
If you sought a different solution, could you explain the requirement with screenshot of the map with flow arrows?
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