Hi BCJ,
OpenGL is not some software you can install on your PC. It is a capability of your hardware. Either your hardware accelerates OpenGL or not, and you can't do anything to it except buying new hardware.
The good news is that most if not all current video cards support OpenGL.
If FlightGear runs, it means you already have OpenGL support. The bad news is "Intel R HD Graphics" is notorious slow with OpenGL applications and I'm afraid you can't do anything to fix this. "Intel R HD Graphics" are great to build a PC using little money, but this PC won't be able to run many games fast. Just in case, check you've got the last "Intel R HD Graphics" drivers and deactivate as many FlightGear features as you can: minimum settings, minimum LOD (
http://wiki.flightgear.org/Level_Of_Detail_(LOD)_Ranges ), fly simple aircraft...
If you are considering buying a new video card, NVIDIA is probably the best option. Not because they make the best video cards, but because FG developers only have NVIDIA cards and test their new developments on them.