Can Reverse Flash kill Flash? Does that mean they can kill each other at any time?
Or is there some particular time point, before which they can't irreversibly damage one another.
Is this time related to a "Missing Flash" newspaper?
The Reverse Flash can kill the Flash, but he does not want to. After the Reverse Flash was stranded in the past, he had to switch gears. His plan was to kill a young Barry Allen, but he failed and found himself unable to use his speed to return to his era. As such, his priorities shifted from killing Barry to nurturing him into a Flash that can then be harnessed to fuel the Reverse Flash's speed. This then would enable the Reverse Flash to return to his own time.
Another one of his priorities seems to also be a careful maintenance of the timeline, Reverse Flash needs some events in the future to still occur, likely to ensure that his era is as he left it. Why/how killing young Barry was compatible with that is a mystery.
No. Well, Reverse-Flash can't kill Young-Flash at any time.
The Reverse-Flash apparently needs Young-Barry to not only become the Flash, but to achieve some sort of level with his powers. This is why Wells has been training Barry to run faster. This is likely because of the Speed Force which the Reverse-Flash currently has access to. If Barry does not become the Flash or achieve full use of his powers, it would potentially create a paradox where the Reverse-Flash also never gained his own powers.
Backing this up is Reverse-Flash's conversation with Eddie, where Eddie deduces that Reverse-Flash didn't kill him back in December due to their connection. Reverse-Flash states that Eddie is his "insurance". If anything were to happen to Eddie in the upcoming battles, the Reverse-Flash would likely cease to exist.
Reverse-Flash could, however, kill the Flash from the future at any time.
Well i see that the other guy have covered the could he kill the flash part nicely however is it related to the event in 2024? short answer: not really.
Long Answer: In the comics the Barry Allen dies trying to stop anti monitor universe no actually a multiverse eating being who has eaten thousands of universe becoming stronger after each one. So that would be the writers plan if they make it to season ten they then would kill of Barry and wally west would take over as the flash. In the comics wally west is hit by an anti matter beam which reduces his speed down to the speed of sound but it takes away his pain in running.