Is there any cookie available for downloads.f5.com site to automate the downloads through script. Similar to Oracle site cookie "Cookie: oraclelicense=accept-securebackup-cookie"
The answer is NO - and why exactly are you trying to automate downloads?
Remember that the actual file you download (e.g. F5 ISO images, attack signatures etc) are stored in AWS S3 buckets corresponding to the region you choose and these do not need any login, you just need to know how to download files from AWS S3