LLC #1 wants to open an account. The sole member is LLC #2. LLC #2's sole member is a revocable trust. A single member LLC can have an SSN (rather than TIN) if the LLC is treated as a pass-through entity. In this situation, is it okay to use the SSN of the trust for LLC #1's TIN?

A single member LLC that is disregarded for income tax purposes can use the TIN of the member. (The TIN may be an SSN or an EIN.) As I understand your question, the trust happens to use an SSN. It could be used for both LLC's.

As an aside, for BSA purposes your due diligence should rise to the level of identifying the beneficial owners of the LLC; i.e. probably the grantors of the trust. My own suggestion would be that you also try to devine the reasons why this double blind mechanism is necessary.