Flame Man is the Robot Master you'll want to take out first. If you go after the guy with the Rush Jet first, you'll lack the Rush Power, which is needed to find a number of secrets in the game. So Flame Man is the best place to start.
Stage: oil field
This is a pretty straightforward stage, but there are some things you need to be aware of in order to stay safe. First and foremost, there are oil pits throughout the stage. The oil will slow you down but you can move through it safely. However, there are enemies that drop fireballs throughout the stage. Flames that hit oil pits will set them ablaze, and burning oil is instant death if you touch it, just like touching spikes.
The other thing to be aware of is the "lobbing" robots that lurk near the ground. These odd fellows can't be hurt with normal arm cannon shots, but a fully-charged Mega Buster shot will cause them to flip and blow up. If they flip into an oil pit, they'll turn into a jump-activated platform you can use to cross safely.
Robot master: Flame Man
Flame Man himself isn't too tough to beat, another good reason to go after him first. He has only two attacks: sending up pillars of flame, and shooting smaller fireballs toward you. The pillars are easy to dodge, just stand between where they're going to form. They're always equidistant from one another, so it's not too tough to pick out the safe spots. The fireballs are ridiculously easy to jump over. Just thrash Flame Man with your Mega Buster and he'll bite the dust before long.
If for whatever reason you beat Wind Man before coming here, Flame Man is weak to the Wind Storm.
Victory here gets you Rush Power, vital for unlocking Beat and finding some other hidden items here and there.
Re-visiting the stage
There is no real reason to re-visit this stage. If you come back with both Rush Power & Jet adaptors, you can get a 1up and a large E-capsule.