UPDATE - 30th Nov '18 - The limitation is now 250 domains. If you have more that 250 sites on Cloudflare, the transfer interface will list only 250 domains in alphabetical order but, strangely, not starting at the letter A - in my case they start at the letter D. You cannot transfer domains that do not appear on the list.
The thread goes on to discuss a number of related issues, with useful contributions by Cloudflare employees.
========= Original Post =========
It appears that Cloudflare accounts with more than 20 sites will be unable to use the new Cloudflare domain registrar service, even to transfer in a single domain.
As currently designed, you have to select the sites whose domains you want to transfer to Cloudflare from a list that the system creates by using the API to get the names of all the eligible domains already using your Cloudflare account for DNS etc. This makes sense, as you can only use Cloudflare as registrar for domains that are already using the Cloudflare service. I presume the list also excludes any sites whose TLD Cloudflare cannot yet handle.
Unfortunately, the Cloudflare API cannot fetch more than 20 sites. You might have noticed the same limitation when submitting a support ticket to Cloudflare: they ask you to select the domain your problem is associated with, but it can only list your first 20 sites (alphabetically).
In the case of the support tickets, it fails gracefully - you can go ahead and submit your ticket without selecting a site. In the case of the registrar service, however, the system throws an error and does not even create a selection list based on the first 20 sites in your account. All you get is a big red error, mentioning the first 20 sites in your account. There is no way to proceed.
I presume that most casual Cloudflare users have less than 20 sites, but I guess that the new registrar service will be of most interest to more serious users with a larger number of sites. To avoid a support nightmare, it might make more sense to at least give users the option to type in the domains they want to transfer in, and then have the system run checks to see which domains in the submitted list are eligible, then display the list of eligible domains and allow the user to go ahead and confirm the ones he wants to transfer.
To be clear, I am not suggesting that users be allowed to transfer hundreds of domains at a time, I am simply pointing out that, as currently designed, users with more than 20 sites are unable to transfer even a single domain.