From what Wikipedia says it doesn’t look like he’s at Flash level.
Hyper Sonic has only appeared in Sonic 3 & Knuckles. He glows with the colors of the Chaos Emeralds, is surrounded by flashing sparks and leaves afterimages in his wake. His abilities are the same as Super Sonic's, though he can breathe underwater and has the added ability of a devastating lightning attack, aka Sonic Boom. This can be used to "double jump" in any direction and when performed, destroys all enemies on-screen, except bosses, with a bright flash. Unlike the game's Lightning and Flame Shield, the player may choose the direction of Hyper Sonic's second jump by holding a direction on the D-pad.
Hyper Sonic, as well as Hyper Knuckles and Super Tails, is acquired by obtaining the 7 Super Emeralds by completing the Super Special Stages. Note that in order to get the 7 Super Emeralds, a player must first gather all 7 Chaos Emeralds, which then allow access to the Super Emeralds.
The reason for the Super Emeralds and Hyper Forms stems from the fact that Sonic & Knuckles is essentially its own game and has its own set of Chaos Emeralds programmed within it. When combined with Sonic 3, the extra Chaos Emeralds from Sonic & Knuckles now become part of Sonic 3 and as a result, something had to be done about them. Hence, the "Super Emeralds" and the Hyper forms.
Storywise, the Super Emeralds were created when the normal Chaos Emeralds and the Master Emerald were all in the Hidden Palace and they all charged each other, the circulation or infinite power made the Chaos Emeralds grow larger and more powerful, but the power was eventually absorbed back into the Master Emerald, along with the power that Hyper Sonic, Hyper Knuckles, and Super Tails had obtained. (Some fans believe that Chaos Control brought the Super Emeralds to Hidden palace, or that two sets of Emeralds combine to form the Super Emeralds, this comes from the idea of two sets of Emeralds. Which is very clearly stated in the English manuals, and is hinted at in the Japanese ones.)
Hyper Sonic or the Super Emeralds have never appeared or been referenced in any Sonic game since Sonic3 & Knuckles.
It is highly unlikely that they will ever return to the series.
Just as Super Sonic refers to supersonic speeds, Hyper Sonic refers to hypersonic speeds.
Hyper Sonic was also the prototypical name for Sonic's upcoming Wii game, Sonic Wild Fire.
From Wikipedia