Limit on Kinesis data Analysis (flink applications) per AWS account

For Amazon Managed Service for Apache Flink (formerly known as Kinesis Data Analytics for Apache Flink), you can create up to 100 applications per AWS Region in your account. This is the default service quota.

For the older Amazon Kinesis Data Analytics for SQL Applications, the limit is lower at 50 applications per AWS Region in your account.

Both of these limits are adjustable, meaning you can request an increase through the AWS Support Center by submitting a service quota increase form if you need additional capacity for your workloads.
Sources
Managed Service for Apache Flink and Studio notebook quota - Managed Service for Apache Flink
Limits - Amazon Kinesis Data Analytics for SQL Applications Developer Guide
Amazon Managed Service for Apache Flink endpoints and quotas - AWS General Reference