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It's not conjecture. Time dilation is a tested, proven effect. You can time travel into the future by moving at very high speeds. That's an undisputed fact.
Yeah, but that's not time travel. That's time dilation. That's a different thing. Time dilation only slows down time, it doesn't let you go back.
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No, no one knows how the kind of time travel presented in 'The Flash' would work, but you can extrapolate from our current understanding of physics and work out scenarios that would be likely, others that would be unlikely, and still others that would be impossible. That's what GOOD science fiction writers do.
That's just guesswork. You don't know that it wouldn't work the way it does on the show, so you're not qualified to say that the show is "getting it wrong" or that time travel has to work the way you think it does.