I'm a writer trying to portray a polyamorous triad between my three main characters. Is there any advice you could give about how these feelings develop?
As far as I can say, romantic and sexual feelings develop for triads about the same way they develop for pairs. It's unique to every individual, but there will be those butterflies, flirting, trying to suss out mutual interest, etc. that you typically see in a budding romance. Then, forming the triad will take some communication and intentionality, but there's no special secret ingredient that goes into polyamorous attraction.
Some other writers have put together guides on writing polyamorous characters - remember that people can only speak for their own individual experiences, so be informed and intentional and never rely on one single source!