My google and forum-fu have not unearthed the answer to this query, so I shall leave it here for discussion and hopefully clarity.

Are the solo and squad mode abilities in First Founding tied to the appropriate first founding chapter, or that chapter and their successors?

e.g. Is the solo mode "Descent of Angels" on p44 for Blood Angels only or can say Flesh Tearers benefit from it?

I've ruled conservatively as a GM, the modes being available in a book called "First Founding" and the background text surrounding the abilities appearing to be about those specific chapters. But I'd like to hear some more opinions.

I'd say yes except if the successor is extremely different, unique, or well-established mechanically - i.e. the Black Templars would not get Imperial Fists stuff.

For successor Chapters that don't have a lot of rules sure...at least until Honor the Chapter comes out, which might give them the individualized rules they need.

I also allow the things from First Founding with the successors printed in RoB since almost all the successor chapters have the 'Use the rules for the base chapter with this one (usualy minor) change' line. If you're deviating from the main rules of the chapter then I'd say no.