1. Please refer to Amazon’s documentation about SES and verification settings first.
2. You would then want to come to your Cloudflare DNS settings and add the TXT and CNAME verification records that Amazon provides you with. The records need to be set be in a format like the following in your DNS settings:
TXT yourdomain.com (replace with your actual domain) "fmxqxT/icOYx4aA/bEUrDPMeax9/s3frblS+niixmqk="
CNAME verificationstring._domainkey.yourdomain.com verificationstring.dkim.amazonses.com
The TXT record above is just an example. Please be sure you are using the one actually provided by Amazon SES.
You will receive a verification problem email from SES if you do not have the TXT record set properly. Please check to make sure that you have the correct record value in your DNS settings.