The sentence would be more clear with a comma -- "I don't have any friends with benefits anymore, either."
"Anymore" here means "no longer", implying that the speaker used to have "friends with benefits" but now does not.
Without the context, I can't be sure exactly what is meant by "either" here. It would relate to something that was stated outside the example sentence. Here are two possible meanings.
1. The speaker could be agreeing with someone.
"I don't have any friends with benefits anymore."
"I don't have any friends with benefits anymore, either."
2. The speaker could be adding information to a previous statement.
"I haven't dated in a long time. I don't have any friends with benefits anymore, either."
I hope that's helpful!