For food shops, see our "Eating" page.
Flumet has a wide range of shops including a cashpoint machine, a tourist office, a newsagent, doctor, souvenir shops. For serious shopping, go to Megeve. A good place to start in Megeve is to park at the car park near the tourist office (well signposted). There's a very nice pottery shop just up the road from there.
For ski rental, there are plenty in Flumet and everywhere, but we go to Rey sports -- drive up the gorge towards Arly, turn right at the turning for the Evettes lift and les Saisies, go left at the mini-roundabout towards the ski lifts and it's just on your left. It's friendly, inexpensive, they have good boots, and it's generally not crowded. There are many alternatives. If you prefer to leave your boots and skis at the lifts, and you are ski-ing Espace Diamant, you can use the shop right by the Evettes lift. This is convenient if you are using the bus to get to the lifts. If you are ski-ing Megeve, there are shops that offer the same service. If you are looking for specialized equipment including mountaineering gear, try the very helpful people at Soquet Sports in Megeve, just above the tourist office.
To buy ski wear and ski equipment, there are shops everywhere. A good option if you are looking for inexpensive, reasonable quality gear is the Mountain Store in Passy which is a branch of Decathlon. Stop there on the way to Flumet on the first day -- it's too far to go back just for that. Stay one extra stop on the motorway past Sallanches, exit at Passy, go left at the exit ramp and it's right there. Normally open till 7, and it has a toilet and cafe as well. When you've finished, take the motorway back one exit and continue to Flumet.
There is a petrol station opposite the big Intermarche supermarket at Praz. There's also a small petrol station very near Flumet: drive down to the main road from the chalet but turn right (away from Flumet), go up the hill; it's a short distance on the left.