Start by accessing the RKI COVID dataset, which is typically available in formats such as CSV or JSON from the RKI's official data portal. Download the dataset to your local machine or a server where you have sufficient permissions to process data.

Once you have the data, inspect it for compatibility with Redshift data types and structure. You might need to clean the data by removing any unwanted columns, normalizing date formats, and ensuring numeric fields are correctly typed. Use tools like Python or shell scripts to automate this cleaning process.

Define a Redshift table schema that matches the structure of the cleaned RKI COVID dataset. Use SQL commands to create the table in your Redshift cluster. For example:
```sql
CREATE TABLE rki_covid_data (
id INT,
report_date DATE,
cases INT,
deaths INT,
recovered INT,
-- Add other columns as needed
);
```

Convert the cleaned dataset into CSV format if it isn't already. This is essential because Redshift's COPY command, which you'll use later, works efficiently with CSV files. Ensure that the CSV is properly formatted with appropriate delimiters and quotes.

Before loading data into Redshift, you need to upload the CSV file to an Amazon S3 bucket. Use AWS CLI or SDKs to upload the file:
```bash
aws s3 cp local_path/rki_covid_data.csv s3://your-bucket-name/
```
Ensure your AWS credentials are configured correctly and have necessary permissions for S3 operations.

Connect to your Redshift cluster using a SQL client or AWS Query Editor. Use the COPY command to load data from the S3 bucket into your Redshift table:
```sql
COPY rki_covid_data
FROM 's3://your-bucket-name/rki_covid_data.csv'
IAM_ROLE 'your-redshift-iam-role'
CSV
IGNOREHEADER 1;
```
Ensure that the IAM role specified has the necessary permissions to access the S3 bucket.

After loading the data into Redshift, perform checks to verify that the data has been loaded correctly. Use SQL queries to count records, check for null values, and ensure the data types align with expectations. Address any discrepancies by reprocessing and reloading the data as necessary.

By following these steps, you can successfully move data from the RKI COVID dataset to an Amazon Redshift destination without relying on third-party connectors or integrations.