Do you have tips on reading handwritten Japanese (that isn't super tidy)? Because someone who never learned any kanji probably understand as much as I do- I just can't decipher which character it is at all most of the time...
Aside from just keeping on reading and getting more familiar with kanji, you could try downloading fonts that are designed to look like handwriting (手書き風フォント) or fonts that look like they were written with a brush (毛筆体フォント) and practise reading with those. Something like アームド・バナナ from the first link might be good. This is the sample from the website:
It’s also worth looking at 略字, abbreviated versions of kanji.
If the writing is just really messy though there’s not much you can do :(