A free program for spaced memorization is Anki

I honestly don`t think that "writing" on you phone display does the trick to learn the correct writing order. I have several apps myself, some of them providing feedback and though it can be fun activity through the day, it does not help me much. Japanese and Chinese are not the only languages that come with learning a new alphabet. Same goes for Russian (and all the other languages of the former UDSSR, like Ukrainian etc.) or Greek. And when you start learning to write your mothertongue, you do so by drill as well. 

It also is a huge difference if you "write" on some kind of display (be it phone or tablet) or on paper using different kind of pens. For example is writing with a ball pen much harder than e.g. writing with a fine felt pen. I for myself started out as I had as a kid learning writing in my mothertongue. A feltpen with a thick tip and a wide pen shaft, looking a bit like those learning ink pens for kids. It may feel a bit weird at first but once you feel the flow of the characters, you much easier understand the writing order and why it is that way. 

Drill is never really fun but I don´t think there is a way to skip that when it comes to writing order. (Though it becomes much easier, when you start writing vocabulary.) Apps and PC programs can be cool to memorize stuff but for writing I don`t think they will ever be able to replace pen and paper. Because it is not only the stroke order but also the way it feels when you do the strokes on paper with (whatever kind of) pen, that helps much more to remember it. 

Hey, just tried this out this app and thought I'd contribute my thoughts on it.

Although this app provides a game-like platform to make stroke order more fun, it removes the characters and words from any kind of useful context. Stroke order seems important for reading and writing anything hand written, but it isn't something a beginner or intermediate student should be dwelling on, as it is a very tiny detail of the language that won't actually help you communicate.

In my experience as a beginner spending your precious study time on something like this just postpones fluency, which increases the chance that frustration will set in and you'll stop progressing altogether. 

Additionally, when an app teaches words and their pronunciation devoid of context, it can't account for changes in pronunciation depending on context! Something very common in Japanese.

I think get the big picture first, iron out the details later.

Although I agree that writing is important, it shouldn't take over reading, listening and being able to answer. This is my main problem in my university class. All we do is write so what happens, we can't talk! There's zero phonetic correction! And as a bilingual person I feel that being corrected early on your speaking skills goes a long way. 

And let's not kid ourselves. When was the last time you handwrote in English? I know I can't remember... 

The reason that kanji exists in Japanese:

漢字 (kanji) is basically just Chinese charecter. In the past, like really really long time ago, when China was rich in culture, (religion, language, how the government worked, etc.) Japan showed their fully respect to China, and even sent people to China for the purpose of learning chinese culture, that's why today there is kanji in Japan. And this is also why people say it is easier for people who speaks chinese to study japanese.