Often, coins don't flip, but instead fall through the spinners and straight into the payout tray. I see people playing the game for the first time who are confused and think they're doing something wrong, especially when the coins fall through repeatedly. If your coin doesn't flip, just keep trying.

The Catch
The casino makes its money on the coins that spill over on the extreme left or right edges, which get sucked into the machine instead of being returned to the player. This fact is not so obvious, because the chutes that take coins which spill over the edges are hidden behind signs that say "Spill Pay Area". These signs have arrows pointing to the middle of bottom shelf, indicating that you receive only coins that spill over the middle, not on the sides.

Basic Strategy
Your coin goes into one of four slots arranged left to right on the front of the machine. Typically there's a left-hand slot, two middle slots, and a right-hand slot. Coins tend to land in front of the slot they're inserted into, so you'll want to play the middle slots. This is Basic Strategy for Flip It. Playing the slots on the sides will mean that more of your coins will land on the sides, and you won't get those coins back when they spill over.

Flip It Myths
Contrary to popular belief, the coins don't keep stacking ever higher and higher. Each machine seeks its own equilibrium for the depth of its stack, and will always return to that depth over the long run. That might be 2 coins deep on one machine and 5 coins deep on another; each machine has its own unique personality, because, after all, these machines are mechanical, not electronic.

Also contrary to popular belief, the casino doesn't come in and scoop out coins once they stack up very high. That's because the coins DON'T keep stacking infinitely, and because the casino makes all the money it needs to on the coins that spill on the sides which aren't returned to the player. These facts are obvious enough with careful observation of a machine, but just to be certain, I confirmed this with an employee at the Four Queens casino in downtown Las Vegas.

Volatility
Machines that gravitate towards shallow stacks have low volatility. You will hit frequently, but get just a few coins when you do. Machines that stack high will have greater volatility: You won't get payouts as frequently, but when you do, they'll be larger. The long run expected return is the same. The machine with the least volatility that I found was the dollar machine at Four Queens, which preferred to be about only two coins deep. The four-deep dollar machine at Stratosphere was much more volatile.

Baskets
Quarter machines have more volatility than dollar machines because the coins are smaller and tend to stack up higher. Quarters played in the middle slots also tend to flip to the sides much more frequently than dollars do, because they're lighter. Since you ultimately lose coins on the sides, you'll lose almost as much money playing quarter machines as you would dollar machines. The one redeeming value of quarters is that they're more likely to flip into a basket (discussed below), although the baskets themselves are nearly worthless.

There are small baskets at the very top of the game, and if your coin flips all the way up there and into a basket, you win the number of coins listed on the basket (usually 10, 20, 50, or 100 coins). On some of the dollar machines, the 50-point baskets move continuously back and forth, left to right, for added excitement. If you hit one of these baskets, there's a bonus round where slot machine reels on the very top of the game spin, and various combinations pay various numbers of coins, with the top jackpot being $2500 or $9999. This jackpot is often listed in an LED marquee to make it look like it's a progressive jackpot, but it's really just a fixed jackpot being advertised with a marquee.
The baskets are nearly worthless. In thousands of Flip-It hands, I hit a basket maybe three times, each time the lowest-payout basket. As further proof, in the six weeks I was in Vegas, nobody hit a 50-point basket at the Four Queens dollar machine to get a reel spin. I know this because for the entire six weeks, the reels were stuck on the exact same combination. (And that was a losing combination to boot, that paid out zero coins for its bonus round.) The machines entice you to play the sides by putting the higher-point baskets on the sides. (Don't fall for it. You won't hit the baskets, and your coins going to the sides of the machine won't get returned to you when they spill.) Note that although I believe baskets to be nearly worthless, you're more likely to hit them on quarter machines than on dollar machines, because the quarters are lighter and flip up higher.

House Edge
I estimated the house edge on the dollar machine at the Four Queens to be about 11.1%. This was based on 405 coins in, 360 coins out, taking about an hour of play, and using Basic Strategy. On any other casino game, 405 rounds would be pitifully small and not at all statistically significant, but Flip It is different. A few hundred rounds of Flip It easily cycles most of the coins in the machine, and it's very clear from playing even 15 minutes that it's an even-sum game, with your eventually getting back all the coins you put into it, except for the ones that spill on the sides.
Because these are mechanical machines, different machines will have different house edges. Machines that flip to the middle consistently will have a lower edge, and machines that send more coins to the sides will have much higher house edge. Also, different machines will have different levels of volatility. One machine may tend to stack four levels deep (high volatility), while another tends to stack only two levels deep (low volatility).

I started to do a trial to determine the house edge on a quarter machine, but I was losing so quickly I got frustrated and gave up. I found that quarters tended to flip to the sides more often than dollars because they're lighter and their trajectory is all over the map. I made a rough estimate that you could easily lose almost as much on quarters as on dollars, just because of all the extra quarters that go to the sides.