I would say it is consistent with someone who hates so much his family and everything to do with them. There are many indications of this throughout the books, I gathered some of them here.
Sirius hated his mother:
[Sirius' mother portrait] "Filth! Scum! By-products of dirt and vileness! Half-breeds, mutants,
freaks, begone from this place! How dare you befoul the house of my
fathers"_ ...
"Yoooou!” she howled, her eyes popping at the sight of the man [Sirius].
"Blood traitor, abomination, shame of my flesh!”
“I said — shut — UP!” roared the man, and with a stupendous effort he and Lupin managed to force the curtains closed again ...
“Hello, Harry,” he said grimly, “I see you’ve met my mother.”
"Your — ?”
“My dear old mum, yeah,” said Sirius. “We’ve been trying to get her down for a month ... "
Harry Potter and the Order of the Phoenix - Number Twelve, Grimmauld Place
and from later in the book:
My mother didn’t have a heart, Kreacher,” Sirius snapped. “She kept herself alive out of pure spite.
Harry Potter and the Order of the Phoenix - The Noble and most Ancient House of Black
When Harry and Sirius examine the family tree tapestry, the disliking was apparently mutual:
"You’re not on here!” said Harry, after scanning the bottom of the tree.
“I used to be there,” said Sirius, pointing at a small, round, charred hole in the tapestry, rather like a cigarette burn. "My sweet old mother blasted me off after I ran away from home — Kreacher’s quite fond of muttering the story under his breath."
Harry Potter and the Order of the Phoenix - The Noble and most Ancient House of Black
He did everything to say he was different from his family
When Harry enters Sirius' room in Grimmauld Place:
Sirius seemed to have gone out of his way to annoy his parents. There were several large Gryffindor banners, faded scarlet and gold, just to underline his difference from all the rest of the Slytherin family.
Harry Potter and the Deathly Hallows - Kreacher's Tale
Sirius almost obsessively hates his family, from a very young age, so I don't see how he can see Kreacher (who was serving the family back then) as something other than a constant reminder of them.
Not really fond of his other family members either
The fact that his brother was a Death Eater and obsessed with Voldemort, wouldn't have made him very happy (He didn't know Regulus changed his mind and tried to destroy the Horcrux obviously):
"Sirius’s brother?” she whispered.
“He was a Death Eater,” said Harry, “Sirius told me about him, he joined up when he was really young and then got cold feet and tried to leave — so they killed him...
Whereas Sirius had sought to advertise his difference from the rest of the family, Regulus had striven to emphasize the opposite. The Slytherin colors of emerald and silver were everywhere, draping the bed, the walls, and the windows. The Black family crest was painstakingly painted over the bed, along
with its motto, Toujours Pur. Beneath this was a collection of yellow newspaper cuttings, all stuck together to make a ragged collage...
“They’re all about Voldemort,” she said. “Regulus seems to have been a fan for a few years before he joined the Death Eaters..."
Harry Potter and the Deathly Hallows - Kreacher's Tale
Actually he said directly he hated all of them:
[Harry] "But . . . why did you . . . ?”
“Leave?” Sirius smiled bitterly and ran a hand through his long, unkempt hair. “Because I hated the whole lot of them: my parents, with their pure-blood mania, convinced that to be a Black made you practically royal, my idiot brother, soft enough to believe them..."
Harry Potter and the Order of the Phoenix - The Noble and most Ancient House of Black
Kreacher constantly mumbling about all this
As for Kreacher, the constant mumbling about Sirius' mother, purebloods and traitors wouldn't have helped in seeing him as just a house-elf.
The elf took absolutely no notice of Harry and the rest. Acting as though it could not see them, it shuffled hunchbacked, slowly and doggedly, toward the far end of the room, muttering under its breath all the while in a hoarse, deep voice like a bullfrog’s, “...Smells like a drain and a criminal to boot, but she’s no better, nasty old blood traitor with her brats messing up my Mistress’s house, oh my poor Mistress, if she knew, if she knew the scum they’ve let in her house, what would she say to old Kreacher, oh the shame of it, Mudbloods and werewolves and traitors and thieves, poor old Kreacher, what can he do...
Harry Potter and the Order of the Phoenix - The Noble and most Ancient House of Black
As for speculation, probably the fact that he was forced to stay in the house he so much hated, with constant reminders of his family wasn't really helping him see things from a more calm and logical perspective.