Can I make chili oil with fresh chilies?

I assume you mean Chinese chile oil, in which I have only seen dried chilies used. I typically want mine to last for months, and I would worry fresh chilies could spoil much more quickly. You also heat the oil a good bit before pouring it over the ingredients, and so you'd need to be very very careful--fresh chilies would have moisture.
I use Fuschia Dunlop's recipe, but I add Sichuan peppercorn:
https://www.seriouseats.com/recipes/2013/02/fuchsia-dunlops-chilli-oil.html
I like a mix of plain sesame oil and peanut oil.

Not all the recipes use dried chiles.
Here's a recipe for preserved chiles in oil which also gives you chile oil.
The homemade oil lasts about 6 months.
https://itsnotcomplicatedrecipes.com/preserved-chillies-in-oil/#wprm-recipe-container-448
If you want another chile condiment, you can make homemade hot sauce from fresh chiles, and keep it a short while in the fridge or longer in the freezer.