Belief systems don't necessarily have to have flaws because belief systems don't require justification. They are simply choices which are made.
They are called belief systems for a reason, not Truth Systems, and everyone has one, and they all have one or more fallacies as their basis.
They resort to circular reasoning, they are self supporting.
This does not mean they are incorrect, fallacies are not a guarantee of being incorrect, just of being beyond the rules of logic.
A fallacy is a weakness that should put doubt in the mind of the believer.
This doubt needs to be overcome, or at least realized and accepted.
A very strong believe system may have only one fallacy, a very weak belief system will be a house of card, teetering on 3 or 4 fallacies.
From my experience representatives from all belief systems will deny they have fallacious beliefs, not all representatives, but some.
Most religionists recognize this. They realize their beliefs are built on the words of god, or their sacred text, or supernatural experiences other have not experienced.
Atheists are different.
Many, certainly not all, maybe not even most, are in denial.
They do not admit that a lack of proof is not proof, and to accept a lack of proof that something is false, is fallacious.
Someone who says 'With science I can show that the supernatural does not exist.' is mistaken.
What they should say is 'Science can not show the supernatural exists.'
'Science lacks evidence to show the supernatural exists, so I do not accept it.'
Science, as a discipline, makes no pronouncement about the supernatural except to say "We have no evidence."
Science is not a basis for morality, and Atheists have moral beliefs, even those who are considered amoral. As they say, even if you do not decide, you have decided.
So for their morality they must go outside of science, they must use some form of circular reasoning to justify their beliefs.
The only way a belief system can be "flawed" is if it is logically inconsistent with itself.
Lets give this a try.
"BeHereNow is the absolute judge of the cosmos, anyone who doubts what BeHereNow says, is immoral, and deserves death. If BeHereNow says something is true or false, there is nothing else to be said. If anyone thinks BeHereNow is incorct on any issue, they are delusional and immoral, and so is anyone who sides with them."
Any logical inconsistency?
An insane person can be logically consistent in their beliefs, does not make them right.