Chihiro has to approach Yubaba and Haku knows this
Any job for Chihiro has to come from Yubaba: most likely she is the only one who can sign on a new employee under a work contract which will give her a degree of status and protection from being arbitrarily turned into an animal or some other cruel fate. Certainly a lowly boilerman doesn't have this authority. So even if Kamaji has some work that Chihiro can do, she will still need have it formalised by Yubaba. And it is Yubaba who is bound by the vow to give a job to anyone who asks, which Haku is well aware of.
However, he needs to buy Chihiro time
When Haku sends Chihiro to Kamaji, the alarm has been raised. His priority is to get her somewhere out of the way where she will be safe, and the boiler room is her best bet: not many people will go there and she won't encounter any scary or dangerous bathhouse guests. Kamaji won't harm her: in fact he protects her by telling Lin that she is his granddaughter. This might conceivably be true, or it might be a ruse, but for it to be plausible Kamaji would have had to be human once. It's likely Haku knows this and is counting on it to evoke sympathy for Chihiro.
Haku probably intends to come back once things have quietened down and sort the situation out then. Either Kamaji will be able to say truthfully he "needs an assistant" and just happens to have found one, or else Haku will be able to use his authority to engineer some other opportunity for her to stay on. Then he will prepare her to approach Yubaba with some degree of protection.
The fact that Chihiro encountered Lin, and Lin was able to be persuaded to take her to Yubaba, was serendipitous. Haku probably did not expect this to happen or that Chihiro would be willing to go with her.