Not really a thrall killing his master would be killed, most likely by the masters heirs or by the master’s servants, but maybe even the other thralls.
Or maybe even by master´s enemies.
Notorious case of Tormod Kark.
Olaf Tryggvason defeated his enemy Earl Haakon. Earl Haakon fled with a single slave named Tormod Kark and sought shelter in a farm named Rimul. The mistress showed them a pig sty to hide in. King Olaf showed up with his army, did not bother actually searching the farm and looking in the pigsty - but held a speech within the hearing of the pigsty, announcing that he
Olaf Tryggvason said:
would reward any man richly who could harm Hákon Earl
Several hours later, with none of King´s men having checked the pigsty, Tormod killed Haakon and presented the head for reward. The problem was, Olaf failed to keep his promise to "any man" when "any man" happened to be a slave killing his own master.
Not every enemy might be so unscrupulous. Best chances for a slave to get away with killing his master is if the master had powerful enemies.
But...
Birchlegs were generally regarded as low status scum. And they won.
By 1170s, were any Birchlegs actual slaves? How did Sverre compare with Spartacus?