Audio Broadcast Flag Licensing Act of 2006 - Amends the Communications Act of 1934 to authorize the Federal Communications Commission (FCC) to require and enforce, in conjunction with the in-band, on-channel technical standard for digital audio broadcast transmissions under consideration, that: (1) all technologies necessary to make transmission and reception devices compliant with such standard are licensed on reasonable and nondiscriminatory terms; (2) such licenses include prohibitions against unauthorized copying and redistribution of transmitted content through the use of a broadcast flag or similar technology; and (3) FCC licensees providing digital audio broadcast service comply with such prohibitions. Mandates the same requirements with respect to FCC regulation of satellite digital audio radio services (SDARS) pursuant to FCC rules. Provides limitations with respect to the adoption of any digital audio regulations.