How can I join a Fortnite clan even though I don't have access to teamspeak or discord or the like?
In general, it is always a good idea to talk to your teammates.
A communication platform (Discord, TeamSpeak) is mandatory for many clans.
In any case, you should consider downloading Discord at least in order to find servers and have a better chance of being accepted.
Depending on which clan you want, I can recommend Fortnite Germany or Fortnite Official.
Many partner Discord servers, such as Trymacs offer a clan search channel.
Just download it.