I strongly prefer the flags. It’s not perfect, but it is both fairly accurate and educational.
In the case of India or a similar country, if Hindi or another language located within an already-represented country (Scots Gaelic in the UK, for example) gets added later, it should also have the national flag. Users are pretty smart and will quickly figure it out.
Can you just leave politics out of it?
I do think this is a legitimate issue for certain languages.
The Indian flag representing Gujarati is the most obvious problem, since that is not the language most immediately associated with the whole of India (that would most likely be Hindi). There is likely to be confusion should languages such as Hindi or Tamil be added in the future.
This issue is sometimes resolved by blending the different flags, often diagonally separated, such as UK/US, or Portugal/Brazil (LingQ does it, in this case!). Of course, that doesn’t account for languages spoken in many countries, perhaps most obviously Spanish. Blending e.g. Spain and Mexico would only highlight the exclusion of other countries even more.
One observation I would make is that LingQ already does make somewhat political choices in their flags: e.g. Belarusian is represented by a flag associated with the opposition, rather than the arguably illegitimate Lukashenko regime. Persian is represented by an Iranian flag (note that Persian is also spoken in Afghanistan and other places), featuring the tulip-shaped “Allah” emblem, but not the religious writing in the seams. Latin is represented by an anachronistic SPQR flag, rather than e.g. the Vatican (where it is still an official language).
I think the flag icon is preferable even for countries like India where there are several major languages. In those cases, the Indian flag (for example) would just be on the list a couple of times instead of just once.
The best viable alternative would be to get rid of any icon whatsoever and just have the list of languages, but that seems comparatively boring and unnecessary IMO.
Spend more time language learning and less time getting offended over nothing.
Damn! I did the (2). I feel so bad, so so bad. I go binge eating now so I can feel better. 
That is what I call an epic pwnage 
Invoking “woke” is not necessary. If someone cares about this issue, they care for whatever reason. I think it would be great if the symbol could be customized. I’d go with the flag personally, but it would not bother me if someone didn’t.
Even later to this party, but I’ve actually been thinking about this issue myself. Regarding South Africa especially, there are several risks where if we wish to add all 11 languages in the future. If we wished to go away from the national flag format, it might end up with adopting flags that are more closely or immediately associated with separatist movements.
Not going anywhere political with that, I just believe if the first association one makes with a flag is a political theme, it might stir up more controversy. Just as this thread has proven, is a real risk. I personally think the ideal might be to actually have the national flag associated with all languages. Ideally, a state is supposed to be representative of all of its people.
Gujarati might not be immediately associated with the Indian flag as Hindi does, but the Republic of India is supposed I think to represent all of its people. Same goes for Afrikaans, isiZulu, isiXhosa and the South African flag.
However in regards to Swedish, personally I wouldn’t be offended by the usage of the meänflakku to represent Meänkieli, but this again opens the difficulties if we would wish to add Elfdalian, since they don’t have their own flag. So maybe the Swedish flag for Meänkieli, Elfdalian and so on would perhaps be best?
LingQ is also very niche of a website, I think adding ISO codes to represent the symbol of a language is going to just alienate the more casual learners of languages.
That’s a good idea based mostly on the representation accuracy, but bringing up the political arguments made a huge disservice to it. Alternative representations may even become a necessity if LingQ expands on the amount of languages offered, but now there will be quite an issue trying to dissociate it from politics.