Could they escape easier? Were they relegated to certain positions? Punished for their unique appearance?
This was a super interesting question, so I went and dug up some info.
For your first question: No, they couldn't have really escaped easier. This isn't really a question of history, but more of a question of albinos. An Albino African would look like a pure white African, not like a European.
True albinos are also exceedingly rare, meaning that there really wasn't any 'general consensus'. While some historical documents (including the one I'm linking) say that it's not rare, they are including both Albinism and vitiligo in their counts, of which vitiligo is much more common. Albinism comes with several health issues, the most significant being eye issues and inability to deal with the sun. Despite this, Joseph Jones, who was a doctor, wrote about them briefly in 1896. He theorized that because of their skin tone, they were 'superior'. Still Negros, but closer to Europeans in intelligence. He also had a whole lot of other incorrect ideas, about a baby being black before developing albinism in the womb, and thinking that Vitiligo was directly related. He wrote about that in "Observations and Researches on Albinism in the Negro Race", which is good for getting at least a rough idea about thoughts at the time.
You can find that article here.
Of the stories mentioned, some seem more accurate than others. The explanation of 'Robert Crews' has him working as a slave, overly sensitive to sunlight, and eventually buying his own freedom due to his intelligence. It's difficult to say if he was treated kinder because of his albinism, or if he simply had a kinder master then others.
The story of Henry Moss is almost certainly fabricated. It recounts the story of a man who developed vitiligo, which eventually completely covered his body. While this is possible, the explanation that his hair turned 'silky straight', and that he was impossible to tell from a European is extremely unlikely, if not impossible. In his case, generous benefactors gave him money so he could buy his own freedom.
While I couldn't come up with any answers directly linked to the American south, around the 18th and 19th centuries there was a demand for albinos in freak shows. The 'white negress' was the most popular, with Amelia Newsham, a slave in London, being one of the more prominent ones.
FYI: slaves didn't need to be albino to be basically white. A lot of slaves were very pale, given that many enslaved women had children fathered by white masters. A few generations of that and children might be indistinguishable from someone widely accepted as being white. Since slave status was inherited through the mother, if an enslaved woman had a child, that child would be enslaved, regardless of appearance. In 12 Years a Slave, Solomon Northup mentions he saw slaves that were "white'. But yes, it was easier for them to escape, since any unaccompanied black person was frequently asked to show their pass--there was typically a hefty reward for any escaped slaves, so people were enthusiastic about searching for them.
On the fiction side, Mark Twain wrote a novel called Pudd'nhead Wilson, about a child born into slavery who is switched at birth with the child of the slave's owner. In part he satirizes that there might be no distinctive difference in appearance between a black slave and a white master.
*edited to fix stupid typo.
I just want to direct you to Charles W. Chesnutt (1858-1932). He has some excellent works (some short stories, some novels) concerning "passing" in the deep South. Definitely worth the read if you are truly interested in what it meant to look white, but be black, in that time period. Chesnutt himself was of mixed races.
Working through an MA at an R-1 here, I study slavery in the upper South. Everything I have read in the slave narratives about albino slaves indicates they were treated like any other slave. Some of those slave narratives are online and you can look through them yourself ---> http://memory.loc.gov/mss/mesn/050/050.pdf I'm reading some Eugene Genovese too, and according to him, chattel slavery in the South was ultimately based on class, not skin tone.
(i dont know if this comment is allowed) but you may be interested into also looking at how multi racial slaves were treated. and after slavery in the segregated south. the concept of "passing" (as a white person) is a pretty interesting topic!
I don't know about albino slaves per se, but I've read the narrative of a similar case. William and Ellen Craft were slaves in Georgia. She was light skinned enough to pass as white among people who didn't know her. The more she and William thought about having children and raising them in slavery, the less keen they were on the idea. Both of them had been mistreated in their own youth, with William enduring the stereotypical sold at auction experience.
So they hatched a plan. William saved up some money from working as a carpenter and item by item bought Ellen a disguise. She dressed up as a young white man going North for his health and taking his faithful slave valet with him. They boarded a ship and sailed to Virginia, where they picked up a railroad that took them most of the rest of the way to Pennsylvania.
Their success making it out of the South speaks for itself, but circumstance did them one better. On the train, Ellen had a few women who took an apparent interest in her. It's been a while since I read the narrative, but I think she even got invited to come calling at the family home when she'd completed her recuperation. There are some other very funny moments mixed with the hard reading of period racism and slave life realities.
A few years after the Crafts landed on Boston, they had to run again. The Fugitive Slave Act of 1850 became law and people came up looking for them. They eventually fled to the United Kingdom rather than risk kidnapping, legal rendition back to Georgia, or setting a bad precedent by letting the Boston abolitionists buy their freedom.
The narrative is available on Gutenberg.