Updates: Added Astro Digital and Planet Labs at bottom.
There isn't a specific Linux distribution for spacecraft. At least not yet. I have heard of groups that basically took Buildroot to build only as much Linux system as they needed for a satellite. Beyond that, they needed to provided the customized middleware or applications.
It is tempting to put Linux on a low-cost small satellites (i.e., CubeSats), one needs to remember that these satellites have extremely tight power budgets, dictated by how much power they can muster from photovoltaic panels. That is, this is an environment in which code efficiency and low power consumption far outweigh programmer productivity.
As for groups working on Linux in spacecraft, here are a couple that can be publicly discussed -- Tyvak (actively) and Boeing (because NASA and AF require it). (And now I've added Astro Digital below.)
Tyvak Nano-Satellite Systems maintains its own Linux distribution for flight software. See: Tyvak capabilities
They have built radiation-tolerant boards for CubeSat avionics. In fact, they use to have a specific ARM-based space avionics board on their website, running Linux. But I don't see it by name anymore. (I recall the name "Intrepid"; someone might find this in some published research papers.)
Boeing recently got the contract to develop a High Performance Spaceflight Computing (HPSC) Processor Chiplet for NASA and the Air Force. The chiplet is to be a quad-core ARM Cortex-A53 using rad-hard by design (RHBD) standard cell libraries. The software requirement for the chip is to run a combination of Linux and real-time OS. The Air Force wants this for their advanced satellite designs. NASA knows it needs advanced processors with greater autonomy capability in deep space robotic as well as human spaceflight missions. See:
Boeing to develop next-generation radiation-hardened space processor based on the ARM architecture
There are a couple of other commercial CubeSat companies that I believe use Linux in their satellites, but I can't readily find this on their web pages. For what its worth, the two I'm thinking of both do Earth observation, and have large server farms on the ground.
Update: one of the other companies I had in mind is Astro Digital; their former name is Aquila Space. Their Corvus-BC has (or did have) Linux running on ARM Cortex-A8. Aquila Space slides from 2015 About a year ago, I attended a talk by Astro Digital, where one of them said even the aerospace engineers (non-computer scientists) could program the spacecraft because they were using Python. I raised my hand to check. "Wait. Python on the spacecraft?" Yes. I grinned as any serious Pythonista should at this point. :-) Note that as CubeSats go, the Astro Digital spacecraft are pretty large. They have 6U and 16U designs, with solar panel arrays geared to feed them.
Update: I also had in mind Planet Labs, now simply known as "Planet". Turns out there is a Space Stack Exchange question that addresses this. They have their own internal distro that they tweak for their fleet of satellites.