While I have my own take on this concept, it's certainly not my original idea as Bramblepaw getting named Brambleflower to honor his mother Goldenflower instead of Brambleclaw after his father Tigerclaw/star is actually a popular reimagining of his character and storyline. Him choosing to become a healer instead of a warrior or first training as a warrior, being named one and then deciding to heal his Clanmates instead just sounds like such a wonderful idea to me. The second path is what his half sister Mothwing did in canon as well. This paired with him and Squirrelflight (and Leafpool) having a sibling dynamic also seems to be such a fitting combination to me. Of course, that doesn't have to mean he'll never have kits though as one more forbidden medic romance in this series doesn't make much of a difference at this point as there are quite a few already.
So here's a bit of fanart (not by me obviously) to properly illustrate fanon Brambleflower as a healer.
By: featherheartwarriors
Characters: Brambleflower (Brambleclaw), Squirrelkit and Leafkit
By: featherheartwarriors
Characters: Brambleflower (Brambleclaw), Spiderkit, Shrewkit, Whitekit, Squirrelkit and Leafkit
In this scenario Spiderkit, Shrewkit and Whitekit are born around the same time as Squirrelkit and Leafkit.
And here is my version of a sign Cinderpelt received from StarClan which told her to take on Brambleflower as her healer apprentice and future successor:
It showed her standing in an unfamiliar camp* on a sunny day in Greenleaf**. The clearing was deserted but she could her cats moving around in the dens surrounding her murmuring softly and purring loudly. Meanwhile, bramble bushes all around her were in full bloom and even when it suddenly turned dark and the night engulfed everything in darkness, the peaceful atmosphere never changed once.
*Cinderpelt had her vision in the new ThunderClan camp at the lake territories.
**Apparently bramble flowers bloom in summer (Greenleaf).