It is a common misconception that a DNS TXT record can only contain 255 bytes. This is not true, a TXT record can actually contain much more than 255 bytes.

rfc1035 defines the <character-string> string object, which consists of a length octet (byte), followed by n bytes of text. There is no null terminator. So, the maximum length of the <character-string> is 255 bytes of usable text.

However, a TXT record can contain one or more <character-string> objects, which the DNS client will stitch together into one long string. For a standard DNS record, the length is ultimately limited by the rdlength property of the resource record format (rfc1035, sect 4.1.3). The rdlength is 16 bit unsigned, so the maximum payload length of a resource record is 65,536 octets (64kb). Keeping in mind the overhead of the length octet in each <character-string> object, you'll end up with a maximum of 65,280 octets of usable characters in the TXT record.

This will work, but requires the DNS server to respond to TCP requests. UDP connections that are more typically used for DNS have a limit of about 1500 bytes in length.