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While you can use some Navigraph FMS data with FlightGear, [1] you could very likely not use the charts within FlightGear.
Definitively not out of the box. From skimming through some documentation and forum posts, when used with MSFS2000 it seem to require a paid plugin, FSUIPC v7 beta. [2] It will unfortunately very likely not work with FlightGear.
FlightGear however can be used together with the
VATSIM ATC network through the
Swift client. [3]
There is also a ATC simulation plugin for FlightGear,
Red Griffin ATC, but it is much less complete than Pilot2ATC. [4]
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[1] See the FlightGear wiki article and section Route manager#SIDs and STARs (permalink)
[2] Dave-Pilot2ATC (August 19, 2020), Installing Pilot2ATC to work with MSFS 2020, Pilot2ATC Users subforum in AVSIM forums.
[3] See the FlightGear wiki article Swift (permalink).
[4] See the FlightGear wiki article Red Griffin ATC (permalink).