Your betta has pretty advanced fin rot adn is bloated.. is his eye cloudy? That would also be an infection..
More info please: http://www.bettafish.com/showthread.php?t=49233
But based on what you said, I have some concerns..
Most people will tell you that you can't ever fully cycle a tank under 5g, despite your filter, and you will always need these changes.. you can try, but careful daily monitoring and reliable test kits should be used. This is for tanks 2.5G+. Anything less and there’s no point in even trying. You need to be testing daily with a reliable drops kit for ammonia and nitrite and doing an extra 50% change any time you see either. In addition to this a weekly 50% with siphon or new fresh turkey baster that has never seen chems is needed to remove poop and other debris from the gravel. It is not enough to just scoop water off the top ever. I actually suggest a turkey baster or very small siphon because your tank is so small an average siphon will remove water too quickly.
First you will see ammonia, then nitrite. Eventually, hopefully, you will see ammonia fall and stay at 0 even after a week of no water changes, and finally nitrite. At this point you will be left with only nitrates after a full week of no changes and these can be kept <20ppm by twice weekly 50% change with baster/siphon. However, cycling will take up to two months to complete and many if not most people will tell you that you can't cycle a tank of this size and you will always need twice weekly 50% and 100% water changes or you will always see ammonia continuing to build and the cycle will never finish..
Bettas are tropical fish and must be kept at a temp between 76-82, with 78-80 being ideal. The temp must be stable and not be dipping or jumping around. In a 2 gallon you can get an adjustable 25w heater. Any new heater should be tested for 24 hours in similar size container with in tank thermometer to make sure it will hold a constant appropriate temp between 78-80F. Then the betta must be acclimated to higher temp either by floating in a cup inside the main already fully heated tank for an hour, or by adjusting the heater to increase the temperature of the tank no more than a degree per hour and 5 degrees per day.
Flakes aren't good nutritional value, and especially with something this small they muck up the water quickly causing excess ammonia. You should look for a good quality pellets whose first two or three ingredients are whole fish, not fish meal or wheat. He should be fed two small meals a day (how many depends on the pellet you pick up) and one fast day a week.
It seems like feeding and water quality is an issue.