Can an IRA invest in a family limited partnership that purchases a life insurance policy on the life of the IRA owner?

Maybe, under limited circumstances. Check out DOL Opinion Letter 2000-10A.

The advisory opinion deals with prohibited transaction issues. Implicit in the question is another issue: whether ownership of an interest in a partnership that owns life insurance violates the rule prohibited IRAs from holding life insurance.

I think this product is being marketed, but there is an issue (in my mind, anyway), as to whether or under what circumstances the intervening partnership, llp, llc, whatever, is a legitimate way to avoid the life insurance prohibition.

I read 2000-10A but it really does tell me if your can avoid IRC Sec. 408 (a) (3) prohibition on life insurance.

Did you mean to say that the opinion did NOT tell you anything about the 408(a)(3) issue? If so, I agree; it's not a "prohibited transaction" issue and would not even be within the jurisdiction of the Department of Labor.