I don’t know about a site for this in particular, but if you allow me to give you some advice, I think it’s going to be better for you to focus on learning words instead of Kanji readings. The readings will come naturally as you do SRS in Anki and mine words and words.
I’ve been learning for some time now (not that long, though) and I found that this method of learning words instead of readings is more effective than memorizing a Kanji and all their readings. You will have to in the end learn this when you come across a new word anyway, sometimes you won’t be able to “guess” how a word is read (I guess it’s this way until you gain a certain level of confidence in the language)
Taking the examples for this problem from TheMoeWay’s site, learning only readings becomes a problem given how many readings some characters have:
家路[いえじ], 通路[つうろ], 家賃[やちん], 漫画家([まんがか], 小学校[しょうがっこう],袋小路[ふくろこうじ], 素足[すあし],素人[しろうと],恋人[こいびと],日本人[にほんじん], 狩人[かりゅうど]
生, 先生[せんせい], 生涯[しょうがい], 生粋[きっすい], 芝生[しばふ], 生き残る[いきのこる], 生ビール[なまびーる], 生真面目[きまじめ],生い茂る[おいしげる]
Also, if you wish to know how much progress you have done in Anki in regards to Kanji (which I suppose is important to know to know which kanjis one will encounter in JLPT Exams, though I think there’s no more official lists anymore) there’s add-ons that track your progress in Anki and draw a chart with all the characters you encountered.
As an example, here’s the Anki add-on Kanji Table, tracking my progress based on the intervals of the card (Blue to red being blue the highest interval and red the lowest, and white/black-red unseen and unmined cards respectively)
Sorry if my answer isn’t what you looked for. I hope you can find what you need if you feel it’s the best for your growth.