Can this advancement be taken by Blood Angel Successors? The reason for me asking, is that, for example, under Flesh Tearers notable characters in Jericho Reach there is a certain Sanguiniary Priest named Jevael. Is this a typo or maybe a general term how all apothecaries of BA and their successors are named since it is clear from the First Founding that only Blood Angels can be Sanguiniary Priests?

Blood Angels, and all of their Successor Chapters, have Sanguinary Priests within their ranks. Two key factors determine this: the Red Thirst and the Black Rage. Even Blood Angels Successor Chapters that have somehow learned to control these signs of the "flaw", such as the Blood Drinkers (who actually just give in and drink themselves full on the blood of…well, anyone really, friend or foe) and the Lamenters, have Sanguinary Priests to tend to their Battle-Brothers' physical and spiritual needs, though in the case of the Lamenters their Sanguinary Priests are instead referred to as the Calix Priesthood but serve the same function and agenda.

Via table-top, any Blood Angels or Blood Angles Successor army may field Sanguinary Priests.

I would easily allow any blood angel successor to take a sanguinary priest.

Except the blood Angel successor from the 'never-heard-of-before-chapter' with the 'special-solo-mode-specially-designed-for-that-chapter' chapter. (In other words… I don't like power-gaming and abusing rules.)

We’ve got a Flesh Tearer Sanguinary Priest in the campaign we just started. We don’t have a problem with BA successors getting them, as all BA and BA successor Apothecaries are Sang Priests.

BYE

yes, what HB said:  apothecaries in Blood Angel successor chapters are called "Sanguinary Priests".  They have the apothecary's function, plus the added burden of certain ritual duties which are pretty much mandatory for those with Sanguinius' curse…

Zappiel said:

Interestingly too, they take over a lot of the responsibilities for teaching BA initiates the secrets, traditions, and history of the chapter from the chaplains. Since the chaplains are a bit busy seeing to, and being on the look out for, the black rage.

indeed!  good additional point to keep in mind; that's something often overlooked…