You can search far and wide looking for their first appearances....
...or just get the Flash vs. The Rogues tradepaperback from 2009, under this cover by Ethan Van Scriver, with a collection of the first appearances of Flash's most important non-speedster foes.
Collected here are the first appearances of....
Captain Cold would be a driving force in Flash's life...and appeared next in Flash #114 (August, 1960, NOT in the trade, but mentioned so a cover with Captain Cold could be shown!).
Mirror Master was the first villain readers saw in the newly revived Flash comic....and he quickly returned in Flash #109 (October-November, 1959), also not in the trade, but a cool cover, nonetheless!
Heck, Grodd didn't even make it on a cover of Flash until Flash #127 (March, 1962)....story not included here, but the cover is to get a look at the furry foe of the Flash!
Pied Piper even branched out in his second story (not in the trade), being recruited by Mr. Memory as the Flash foe in Justice League of America #14 (September, 1962) along with Green Lantern foe Hector Hammond, Aquaman villain Sea-Thief, Wonder Woman rogue Angle Man, Green Arrow evil-doer Dr. Davis and (behind the scenes) the Joker (to capture Batman), all while dealing with the Atom joining the JLA; though all these villains didn't make the cover!
Weather Wizard didn't make the cover of his second appearance (Flash #130 of August, 1962, facing Kid Flash and the Elongated Man), but did finally in Flash #145 (June, 1964) in a tale not in the trade.
Trickster quickly strikes back after his heist of a plane in mid-air, quickly coming back to play new pranks on the Flash in Flash #121 (June, 1961) in a story not in the collection.
This boomerang quickly returned, facing the Flash and the Elongated Man in Flash #124 (November, 1961), in his second appearance (which isn't in the trade).
The Top spun onto his first cover on his own with Flash #141 (December, 1963), where we also met Peter Gambi, a tailor to super-villains in a stylish story (not in the collection)!
Heat Wave's second appearance with with all the Rogues, but his appearance after that was in Flash #166 (December, 1966), still facing off against Captain Cold (but not seen in this trade), and Mick continued to be a thread to the Flash, eventually taking him on on his own!
a surprise villain the Rogues faced as well (who tried to make a monkey out of the villains).
The Rogues returned en masse for the second time in Flash #174 (November, 1967), making life hard for the Flash yet again in a story not in the Flash Vs. The Rogues trade, but, like all these stories, proving that sometimes things are better the second time around!