Not much is known about Flugel and Reid's relationship, however, we do know the two of them shared a similar relationship than that of Gian and Suneo from Doraemon series. From what the author had said, it's safe to assume Flugel was the "brains" and Reid was the "brawn" of the duo.
According to Shaula, Flugel alongside "Mother" created her. Shaula spoke very fondly of him, praising him whenever she got the chance to do so. It's also safe to assume Shaula and Flugel shared a similar relationship as Subaru and Shaula did about 400 years after Flugel's disappearance. ShauIa has mentioned that she had deep feelings for him, and also stated that Flugel was often tired dealing with her. It was also mentioned that Flugel would get sick of Shaula's antics and would periodically get annoyed at her.
Similarly to Reid and Flugel's relationship, we know next to nothing about the chemistry between the Sage and the Divine Dragon. Volcanica seems to have been rather close with Flugel as his words regarding him were full of fondness and love.
Petelgeuse seemed to have held the Sage in high regards as well, referring to him as "Master Flugel", apologizing to him for breaking the promise and taking in the Witch Factor of Sloth after Regulus Corneas and Pandora backed him into a corner, roughly one century before the events of the main story.