I play both a secrets mage and a miracle rogue.
As another poster pointed out, secrets mage counters miracle rogue. I like to play decks to counter each other as you get a better sense of the strengths and weaknesses of each class.
Anyway, to beat a miracle rogue, you need to counter the Auctioneer. Most of our plays depend on this one card, so in a sense its actually very fragile.
1. Watch for turn 5 Auctioneer->Prep->Conceal, throw down a Counterspell by turn 4 if you can, preferably behind a Kirin Tor Mage.
2. As you have might have noticed, a flamestrike will kill a concealed auctioneer.
3. After that you need to determine which miracle variant you are playing against. Leeroy Miracle, Spellpower Miracle and QA/EVC Miracle are the 3 common variants.
4. You can tell its a Leeroy deck if he doesn't Shadowstep his Auctioneer, even when he should. The full Leeroy combo does 26 damage out of nowhere, so keep taunts up.
5. For a Spellpower miracle deck, save a polymorph for Malygos at turn 9. Throw a counterspell up at turn 8 to eat the conceal that is coming. Beware of spellpower enhanced blade fury, so play minions that have high health, and don't flood the board. Most spellpower minions don't trade well, so take board control.
6. If he is running the last popular variant of miracle, the QA/EVC version, again you need to save a polymorph. Popular plays include turn 5 Auctioneer->Shadowstep, then turn 6 QA->Auctioneer->Prep->Conceal. To counter this, either counterspell at turn 5 or coin a flamestrike out at turn 6. If you have silence, wait to use it on the QA or the EVC.
Other than the above, it will still come down to draw, so get used to loosing =). Still, being aware of your opponents possible plays should tilt the odds in your favor.