1. Give to the General Fund.
BC's needs our gifts to continue its mission. The general fund covers a variety of areas. This money could trickle back to sports, but the purpose of the General fund is for BC to use the money as it sees fit. Plus even a small gift to the General fund helps the school's rankings and keeps you on the donor list.
2. Give to a named Athletic Scholarship or endowed position.
This way you can give to BC sports but not support the area of the Athletic Department that has upset you. Like the suggestion 1, this can still indirectly support the Flynn Fund, since the money from your gift rolls into the same budget as the Flynn Fund. But the intent is still there.
3. Give a conditional gift.
If you want Spaz gone or Gene gone or something else done, give BC a conditional gift. Say "I will give $XXX when Spaz steps down..." etc. BC is likely to reject this offer, but your point will be made. If enough former givers promise conditional gifts it swill send a message beyond the Athletic Department.
In full disclosure, my wife and I gave to the BC Fund in December. The size of our gift varies from year to year, but we do feel it is important to give to BC consistently.