This could be "Space Warrior Baldios". It's a series aired in 1981, with a movie concluding the story released the following year.
It matches your description of a fleet coming from a dying planet: the invaders escaped their home planet, become almost uninhabitable due to radiation poisoning after a terrible war, aboard a space fortress, trying at all costs to find a new planet.
The time loop element matches too as, in order to defeat the terrestrial forces, the invading army provokes greater and greater disasters (the destruction of Mercury and Venus, the melting of Earth's polar ice caps) progressively making Earths more and more similar to their home world. In the end, it is indeed revealed that the invading fleet moved through time rather than space, and are effectively humans from the future.
I only have some vague recollection of the series and I don't have distinct memories of flashbacks, so I cannot say whether this matches the "rose sequence" or not.