The Flaw in question is Monastic Vows.
Obedience makes sense, I guess, since you need to do as told by the local priest, but what else does it do? A strict inability to seduce enemies is only going to actually cause stories in maybe 1 out of every 1000 sagas, and poverty doesn't cause stories if the character in question doesn't try to fix it, which this Flaw of course forbids.
So aside from having to answer to the big guy in the church (and really, most characters have to answer to that guy on some level anyway, as incurring his wrath is never fun) what stories does this Flaw even force to happen?
What happens when someone tries to seduce you?
What happens when someone in your church thinks that you are not chaste? (Because you keep hanging out with those half naked faeries and Criamon...)
What do you do with your share of the treasure? What if two church factions want it?
What do you do when you need to do something but lack the funds because, you know, poverty?
And then there are some less direct stories....
When the duke and bishop agree that you are the perfect candidate to tutor the duke's bratty six year old twins....
Read some Brother Cadfael books. 8)
The first bit is probably the most obvious hook - "you must do what your abbot tells you to" - and failing that, as you say, the local priest. Basically, it's an issue of split loyalties. What if they want you to do magic on the Church's behalf? Or that priest from Antagonists wants your assistance in incorporating the Order of Hermes as an actual monastic Order for the Church. Personally, if I were a local priest, and I knew that a maga was at my beck and call, you can bet your cassock that I'd have him be doing SOMETHING for the local townsfolk every year. Y'know - just to keep an eye on him. And to put that suspicious "magic" of his to the work of God, not just for his own selfish desires.
In thinking about it a bit more: your character will be the default target for farie seduction and infernal corruption. For faries, it's because it's narratively more dramatic to have a monk be either challenged, or fail a challenge, of that sort. For the Infernal - well, they hate everyone equally, but as a practical matter: corrupting a monk is almost as good as corrupting a priest, in terms of decreasing the population's view of the Church.