You can't find a lot of Asian ingredients on Amazon Fresh or other delivery services.
Amazon (the main site) does sell more stuff, but the prices are ridiculous sometimes.
Ex. Chinkiang vinegar, a very staple type of vinegar for Chinese food. $2 at a local Chinese market. $8 on Amazon.
My grandparents, parents used the gold plum vinegar. As a result, I have used the gold plum vinegar my entire life and no other vinegar matches up: Gold Plum Chinkiang Vinegar, 18.6 Fl Oz (Pack of 1) https://www.amazon.com/dp/B00BUIKGU0/ref=cm_sw_r_cp_api_i_f2LlFbFGCSNTZ
Many different option available on Amazon here in the US. Here’s just one. I prefer this over balsamic, but as you say, if you are using what you have, and you have balsamic, it’ll do!
It's Zhenjiang vinegar. It was $8 on Amazon which is rather more expensive than I'm used to but that might be partly because the cost of living in corn belt Midwest is real low.
Gold Plum is highly recommended https://www.amazon.com/Gold-Plum-Chinkiang-Vinegar-18-6/dp/B00BUIKGU0
One of the most famous and delicious Chinese black vinegars is chinkiang vinegar. I searched on amazon for it and included a link
https://www.amazon.com/Gold-Plum-Chinkiang-Vinegar-18-6/dp/B00BUIKGU0
black vinegar, french mustard
chinkiang black vinegar is so good!!! that's what makes hot and sour soup delicious, what gives xiao long baos/XLBs their savoury-ness, and you can use it for salad dressing to seasoning dishes and even dunking things straight. You want GOOD quality black vinegar, which should be made by fermenting glutinous rice/yeast and vinegar. The process is similar to balsamic vinegar (which is why they can sub for each other), but less sweet and more umami. (think very malty miso fermented and vinegar)
Because of how its processed, the fragrance (ethonals) have a low boiling temp so you want to add it AFTER you've turned the stove off, and stir it in.
I also feel the same about good quality mustard. When I make mireproix, I fry it with a dollop of grainy french mustard; it gives that immediate sense of warmth in any dish and also is slightly acidic so you can use it as a flavour-balancer without using a direct harsh acid (lemon, white vinegar). It also makes a great marinade/tenderizer, enhances potatoes, makes a killer egg salad or just smeared with butter, bread, cheese. It makes the MOST UNBELIEVABLE MELTING CHEESE SANDWICHES
Black vinegar: Chinkiang Black Vinegar
French mustard: Pommery Meaux Stone Jar
These are the two I and my family use. For Shao Hsing that's the name I can see on the bottle: it's a brand of rice cooking wine.
https://www.walmart.com/ip/Shao-Hsing-Shao-Xing-Cooking-Wine-25-OZ-1-Bottle/825631622
For the vinegar, it's Gold Plum
https://smile.amazon.com/Gold-Plum-Chinkiang-Vinegar-18-6/dp/B00BUIKGU0?sa-no-redirect=1
I also made a correction to the fish sauce brands as I mixed 2 brands together. I grew up with these bottles so I don't pay as much attention to the name as I did the images on the label!
Here's the brand I usually buy:
https://www.amazon.com/dp/B00BUIKGU0/ref=cm_sw_r_cp_apa_glc_fabc_PTWNANFHE3SKTFPDRGK2
It will only be a few dollars if you can find it in a shop. Most Asian markets will carry it.