I’d say it’s fine to do both at the same time if you can manage them. For that, I think you need to give them a try and see if you can indeed handle them both 
My opinion is that if you’re a beginner in Japanese, you should go by this order:
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Kanji: start working on getting used to the WK’s routine. Make sure you stick to it. Don’t focus too much on doing things fast, but on doing this steadily, day in and day out. Consistency is King. Read my guide for Wanikani. It has pretty much all the advice you’ll need during your WK journey.
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Grammar: Once you get solid on Wanikani after a few weeks, I recommend starting with grammar. You could know all the words, but if you don’t understand how those same words connect through particles, etc… you’ll have a hard time. The grammar taught to beginners is very very frequent, so it will definitely be a good usage of your time.
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Vocabulary: Assuming that you’re a beginner and your kanji knowledge is limited, I’d recommend going to Kitsun’s Core 10k, then to the manage cards’ table and search for the tag “kana”. This will give you a list with all the words on the top 10000 that are written in either hiragana or katakana. You can select them and add them to the front of the lessons pile. This will give those items priority and display them in your lessons first. Let me know if you need help with the steps on how to do this.
I think 5 lessons a day on kitsun would be more than enough to keep you going. Like I said, focus on making Wanikani work for you and then jump to grammar. You can use the reading tool on Kitsun to start practicing your reading with some beginner-friendly stories too