As a Japanese-speaker, my first reaction upon reading your question was like "Since when is どうやら a verb!?"
「どうやら」 is an adverb ([副詞]{ふくし}) in Japanese even though your source appears to give verbs (to seem, to look like) as its definitions. And because 「どうやら」 is an adverb, it is perfectly natural that it is used together with the auxiliary verb 「らしい」. There is no redundancy there.
「どうやら」 means "not certainly but probably", "in some way", etc.
「らしい」 means "to look like", "to seem like", etc.
These two words are often used together to express an inference based on grounds.
If you said 「[明日]{あす}は[雨]{あめ}らしいよ。」, it would surely be understood but it could sound kind of curt depending on the situation. It would sound like you said it using the fewest words possible. I admit that adding 「どうやら」 will not change the meaning of the sentence much, but it will sound "more normal" or more like human conversation.