What is the best method to migrate 11.2.0.2 database on IBM AIX to Oracle database cloud service (DBCS) ? (Looking for the fastest method)

Zero Downtime Migration service

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1. RMAN backup methodology

2. Transportable tablespace

as long as this heterogeneous platform fastest way is the Trabsportable tablespace.

and to reduce the downtime you can 

backup DB then convert it while source is online then in the cutover take incremental backup and convert it.

you can check oracle note 2005729.1 for more info about Trabsportable tablespace

You can migrate your on-premises Oracle databases to Oracle Database Cloud Service using various different approaches based on different tools and technologies

• Choosing a Migration Method

• Migrating from Oracle Database 11g to Oracle Database 11g in the Cloud

• Migrating from Oracle Database 11g to Oracle Database 12c in the Cloud

• Migrating from Oracle Database 12c CDB to Oracle Database 12c in the Cloud

• Migrating from Oracle Database 12c Non-CDB to Oracle Database 12c in the Cloud

• Migration Methods