In medieval Flanders and Brabant the executioners (of which there weren't a whole lot) were contracted seperately for every job they had to perform and thus paid for seperately for every execution. Why do you see this as a conflict of interests?

This was the case in Melbourne Gaol throughout the 1800s. Sometimes, guards would even get prisoners to volunteer to perform the hanging and pay them for it. Elijah Upjohn, the man who hung famous Australian bushranger Ned Kelly, was one such volunteer. From what I can find in a quick google, he was paid 5 pounds (about $600 AUD today). That number seems high compared to other payments, so perhaps it's not correct, or perhaps Kelly's extreme notoriety meant higher compensation for his executioner.

However, it's also worth noting that there were professional hangmen- Upjohn was only required because the regular hangman was not available, and as a result Kelly's hanging was a lot less “clean” than it should have been.

Another case study is William Banford, who become a professional hangman as a result of performing a couple of volunteer hangings. Even as a professional, however, he was paid per head. This site has some interesting sources on him.

In NSW, though, executions seem to have been paid a salary. Here's another case study. This is William Greene, appointed in 1828 and given an annual salary of 15 pounds 14 shillings 2 dimes, plus accommodation.