From 6.2 on, I've redesigned the flowchart into two types; Serpentine [i.redd.it]and Linear[i.redd.it].
I believe linear to be far easier for new players to follow, while serpentine is more convenient for those looking to get the order of a specific section, or want to see more of the story in one go.

For both charts, I've added a lot of indicators to help add information without overloading the graphic.

• All the non-soloable content has been shifted from the main line of story progression as offshoots. In the linear version this is anything NOT in the central column; for serpentine it's anything not following the main progression line and the arrows have an uneven boarder around them
  
• Anything with a gold boarder is core story - other colored boarders are optional/extra and can be skipped without affecting story progression
  
• Circles are planets where you do missions (solo)
  
• Oblongs are planetary bonus missions
  
• Diamonds are planet-independent content (chapters)
  
• Rectangles are flashpoints (4-man dungeons)
  
• All flashpoints with solo versions are named "story flashpoint" and have rounded corners (plus are in-line with the main story)
  
• Hexagons are daily areas or (if squished) non-standard content
  
• Purple plaques are Operations (8 or 16-man raids); these DO NOT have solo versions
  
• Smaller plaques are Instance bosses = single operation boss (8 or 16m)
  
• The Dreadmaster story is indicated by purple arrows and a small red diamond. This is a side story mainly told (and ending with) operations. NOT solo-friendly