Shiratamako (白玉粉）is sweet or glutinous rice flour, or mochiko, mixed with a little corn starch or potato starch. If you can’t find shiramako, you can use mochiko with about 1 tablespoon of cornstarch or potato starch flour added. You can find all of these flours at a Japanese grocery store. You might be able to find them at a health food store too, since rice flour is more popular nowadays as a gluten-free thickening agent for sauces.
The hardest part of this whole recipe is finding the two rice flours. Look for them at a Japanese grocery store - a general Asian grocery store may not carry them.
If you can’t find joushinko and/or shiratamako or mochiko…
You must use rice flour. Wheat flours or other grain flours will not work!
For the joushinko, substitute regular rice flour - one that’s not labeled “sweet” or “glutinous”. For the shiratamako or mochiko, substitute ‘sweet’ rice flour (one that is labeled ‘sweet’ or ‘glutionous’), which is not actually sweet to taste like sugar; it’s just more sticky. You can find these rice flours at general Asian or Chinese grocery stores, as well as some health food stores. Please note that using these different rice flours will change the flavor and texture of the dango, but at least you will have dango with more or less the correct consistency. (You can even experiment with things like red rice flour instead of johshinko.)
(Edited to add:) Can you use all mochiko? You could, but the dango will be of a different texture, gooey and hard to mix up. Please do try to find the non-glutinous type of rice flour to add to mochiko. I have seen both kinds sold at many Chinese grocery stores, so it should not be that hard to find if you have access to a Chinese or general Asian grocery store.