It is not a requirement that a coach needs to take both certification if you coach both flag and tackle. However, USA Football recommends any coach that is coaching flag and tackle to take both certifications.
We do recommend that any coach that needs both certifications to consider purchasing a USA Football Coach/Commissioner Membership: This includes both certifications ($30 value), accident insurance coverage, youth tackling & contact system and much more for $40 and that can be purchased here USA Football | Membership.