That's one finger. Two finger is thrown with the middle finger. What kind of Innova plastic do you have? There are a lot of different types that fly very differently.
If you are throwing a flip shot (flick, forehand, sidearm) right-handed and the disc is going to the right... neither tipping the disc down nor needing more overstable plastic is the problem. Rather, the opposite.
Flip shots turning right or backhands turning left are natural tendencies for the flight. Beginners almost always face a case of "hyzeritus", not getting a full flight's worth of their throwing power.
There are several factors that control how much in what direction your flight will turn.
1) Angle of release. If the disc is pointed down on release, the disc will hyzer (turn right for right handed flip shot). Angle up will make the disc anhyzer.
2) Pitch on the disc. If the disc is pointed down, it will tend to anhyzer and drop. If the disc is pointed up, the disc will tend to hyzer and rise. Certain upshots requiring speed control can make use of pitch, but flat release is best for most all drives.
3) Spin. The more spin on the disc, the more it will turn over, or anhyzer. Glide and distance are also created from spin.
4) Type of disc. Some discs are so "flippy" they will turn (to the left for flicks) right after leaving your hand. Other overstable discs will hyzer and skip. This is what sounds like is the case with your throw. You say it goes straight for a while before turning right.
5) Other Technique. With a flick shot, "rolling" the wrist can have a dramatic effect on the flight. If you turn your wrist left as you release, the angle of release will be tilted upward, resulted in an anhyzer. Generally keeping the disc flat is a better practice.
Where the release point in relation to the body also has a great deal to do with the flight characteristics.
Throwing with two fingers underneath will generate more power and should keep the disc flatter with more spin.
This might be too much info. and not very helpful. I would suggest throwing your flip shot with drivers and midrange discs of all different stabilities. Figure out which ones turn left and what is making them turn. Balance that in with the throw that's currently turning right. Then you'll know how to get the disc to fly as straight as possible for as long as possible.
I'm just thinking on the spot here. I'm sure there has been many different articles written on technique. Look on the PDGA forum under techniques. If you dig in you will find links to good descriptive techniques. Maybe some golfers on this forum know of some.
I listened to a clinic that Scott Stokely put on once. He had one of the longest flicks on tour. He said to lead with the elbow, then the wrist, then the fingers. This full extension, resembling a sling, will get a lot of spin on the disc. If thrown flat with the right type of driver for your level of power, the disc should go straight for a long way. Sturdy footwork always helps too.