Specific strategies for Japanese - not so much - however, I’m a speech-pathologist, and do a fair bit of work with dyslexia/reading disabilities/literacy, and it’s something I love. I don’t know how much specific dyslexia knowledge you have, so feel free to skip some of this. It’s probably an excessively long rant.
A bit of dyslexia theory
There’s a lot of disagreement in English about what constitutes ‘dyslexia’ (currently DSM terms it ‘specific learning disability in reading’) - when do we know the person has dyslexia, versus (as is extremely common in schools in the US and Canada - can’t speak to other countries) has had poor literacy instruction. Most commonly, dyslexia gets defined as the person having good oral language and poor decoding - sounding out words - and/or poor reading fluency - slower, less automatic reading. Their reading is worse than we would predict based on their other skills.
There is general agreement that vision is not a component - it’s a persistent belief, but doesn’t hold up in most research. Some people with dyslexia report that the letters feel like they’re moving around, but this seems to be more of an effect of how hard the reading task is.
Often there is a phonological component - difficulties processing/breaking down the sounds in words. One theory on that piece is that the person’s ‘mental representation’ of the sounds are kind of blurry - they have a general sense of what that word sounds like, enough to match it when they hear it to get the right word, but if they’re trying to access it more closely, for example to spell it, they don’t really have the details stored well. Another phonological challenge can be difficulty with blending the sounds together and recognizing the word.
The other ongoing theoretical piece (that I’m aware of off the top of my head) is the transition to automaticity. As you read words over and over, they gradually change from words you sound out each time, into ‘sight words’ - you recognize them just by looking at them - I’m sure you’ve seen those sentences with internal letters flipped around that you can read perfectly well - your brain can read those words well enough that they recognize the general shape/form on sight instead of going through the more auditory path of sounding it out. It seems like people with dyslexia have more difficulty and take much longer to transition words from needing to be sounded out to being recognized on sight. Obviously this has a significant impact on how fluently you can read.
People with dyslexia do note that some fonts are easier than others - specifically to help with differentiating letters when they’re trying to read faster etc. As far as I know, Japanese doesn’t have those, but it would likely be beneficial to look for materials with a pretty clear/consistent font to get started (though eventually practicing other fonts would be helpful for accessing different media etc). I’d particularly look for one where similar looking kana look pretty different.
I suspect more repetition, and particularly practice at ‘sounding out’ words in kana will be helpful as far as increasing fluency there. It might be helpful to focus on a few kana at a time (if they haven’t mastered this already), to build up fluency and comfort - it will likely be slower than for some of your other students. I would work the other way too, on typing or writing the word they heard, to help with sound awareness (honestly, probably a good idea for most foreign language learners).
I assume you’re not trying to treat this student’s dyslexia in the club, so I would also look at accommodations to help them keep language learning, even if their reading is lagging behind other skills - trying to do more oral practice, using reading passages that have an audio version available for them to listen along with if reading the passage feels out of reach (obviously their listening level will have an impact here), or even having peers reading the passages aloud together. Generally I recommend that you get input from the person with dyslexia about how they feel about taking a turn reading aloud - some are comfortable, and some really hate it.
And, of course, ask them what else they’ve found helpful in classes or other environments, or what you can do to help support them. Maybe they would like to have some one on one time to sit with you and practice their reading to feel more comfortable, maybe they’d love to have a specific buddy in the club to bring their reading questions to. Maybe they’d just like to do their best for now, and will let you know if there’s help they want. They know how their dyslexia feels on the inside, and are the best expert as far as accommodations/supports that they want to have and find helpful.