I think there are several interpretations, with no definitive rules support one way or another, so it's dm judgement call.
No, flaming sphere stays lit, and pyrotechnics causes the fireworks or smoke
The flaming sphere stays lit and you get the fireworks/smoke.
The reason the sphere stays lit is that it is fueled by magic, not mundane fuel.
While there isn't explicit rules support for this interpretation, it isn't unbalanced because it isn't more powerful than the spells separately, and deciding in favor of the PCs and the rule of cool argue in favor of it.
Perhaps for fluff it goes out during the fireworks/smoke, then relights.
A Contrary Argument
A contrary argument would be that you get either spell, but not both. Basically either one spell or the other wins.
If pyrotechnics wins, then the flaming sphere is extinguished and you get your choice of the fireworks or smoke.
If flaming sphere wins, then pyrotechnics fails to extinguish the flame.
This is making the assumption that the fire in the flaming sphere is magically fueled for the duration, and it seems reasonable to assume that it can't be snuffed the same way as a regular fire, because magic.
So how to decide which spell wins? Assuming they're both cast by the same caster, it seems reasonable to let the caster choose. If cast by different casters in an antagonistic situation, if the spells have been cast at different levels, higher level wins; otherwise, its a contest between spellcasting abilities.
No matter what, the fires created by the flaming sphere are fair game
You can use the flaming sphere to ignite something, and then use pyrotechnics to blow that stuff up like a boss, or, create smoke, of course.
Again, there's not much in the way of rules support, but if you think allowing the sphere to stay lit is overpowered, then perhaps this is the way to go.
Note:
My original answer was significantly different from this but editing it made me re-think it.
Best Answer
No.
The power's description doesn't explicitly mention the Melee keyword for the sphere's attack, therefore that attack is not a Melee attack.
The only restriction is that the attack's target has to be adjacent to the sphere, but a close blast 1 or a [non-provoking] ranged 1 attack has the same effect. This means that the range restriction cannot be used to guess any implicit keywords of the attack in that way.
Compare the wording of these Conjuration powers, some of which explicitly mention the proxy's attack's type:
Flaming Sphere[DDI]:
Mordenkainen's Guardian Hound[DDI]:
Ball Lightning[DDI]: