I think there was some petty jealousy there, sure. But I think his dislike for Buffy went a lot deeper than that; Buffy posed a big threat to everyone in the Initiative.
Before she came along, they were used to following orders, and not asking questions. Demons were demons and needed to be killed. Or saved for parts. Whatever Walsh demanded of them. But Buffy made Riley, the strongest leader among the soldiers, begin to question everything. Their nice little tidy package which told them how to think and act started to unravel.
And Forrest started to lose a friend.