There are two ways to look at this. "Hadith al-Kisa'" can be used for a group of narrations, mostly short narrations, describing the general event in which the Prophet (S) covered Ahl al-Bayt (A) with a cloak and identified them. It is generally agreed that this event took place.
"Hadith al-Kisa'" is also used specifically for the longer narration of this event which is attributed to Fatimah al-Zahra (A) and which is often recited at gatherings today.
I assume your question is about the second one (that is, the longer narration of this attributed to Fatimah al-Zahra (A)).
It is reasonable to say that there are some questions surrounding its chain of narration. However, this does not automatically mean that is fabricated, unless there is evidence or an argument that it was fabricated. There is a big middle ground between "strongly authenticated chain of narration" and "fabricated", and, when dealing with texts that are over a thousand years old, many fall into this middle ground.
(I don't think the "sequence of events" argument is strong enough to declare it as fabricated, since no one today was alive back then to say exactly what the sequence of events was, but everyone is different.)
I would suggest that it is good to appreciate the general meaning of this narration, but not necessarily to hone in on every single word and use every word as absolute proof for the nature of reality, as some people sometimes do sometimes.
For instance, sometimes some people feel disappointed when they are having a personal problem and recite this text in a gathering, but their personal problem is not solved. This is because the text says that whoever recites it will have their problems solved. It is better simply to take that as an expression of hope that Allah might solve their problem, and that, perhaps, by reciting the text sincerely, it might bring them closer to Allah and inspire divine assistance or intercession. (Rather than taking it as a literal guarantee.)
At the same time, today, it has become a sort of customary "requirement" to recite this narration in certain gatherings, and this is also not correct. (If Allah has not required us to do something, who are we to require others to do it, such that we might attack or condemn them if they don't?) It is fine to recite it, or fine to skip it.
Unfortunately we are living in a time where there is a lot of intolerance, some people need things to be absolutely right or wrong, either absolutely correct or fabricated, you either have to recite it all the time or never recite it at all. The reality is, it isn't really possible to apply that standard to much of our textual heritage (apart from the Qur'an) since we are dealing with texts that are over a thousand years old. What can be said is that the text exists, it has become part of the Shi'i custom and perhaps there is a reason for that. There is spiritual merit in reciting it and pondering over it, in any case it should be treated with respect. However if someone chooses to focus on other texts, that is also fine. Either way, they should not be attacked for their decision.
At the end of the day, actions are judged by intentions, and if someone is approaching Allah sincerely in a devotional manner through using a text attributed to Fatimah al-Zahra (A), I am sure that Allah would appreciate that and respond in kind.