To send and receive SMS messages without using a Twilio phone number, developers can use Telerivet as a gateway app with a local SIM and integrate it as a custom channel into Twilio Flex. The solution consists of two parts: receiving a message from a correspondent and sending a reply back to them without having a Twilio number. Developers will need to set up a Twilio Studio Flow, create a Flex Flow, deploy Twilio Functions, configure Telerivet, and handle inbound messages with a webhook API. With this setup, developers can interact by SMS through local numbers in hard-to-reach regions, such as Sudan, Libya, or Madagascar, without relying on Twilio's phone number services.