Not to be too pedantic here but ft/s^2 is not a force it is an acceleration. And the value you site is wrong for the gravitational acceleration at the Earth's surface. It is 9.81 m/s^2, 32.17405 ft/s^2.
Nonetheless; my calculation says that at 9.8m/s^2 it would take 0.95 years to get to the speed of light. This calculation is based on classical mechanics not taking into account relativistic effects.
And taking relativity into account? What then? Earth’s time? Traveler’s time?
Great reply. This means, if one were to accelerate to the speed of lignt, one would not want to do it quickly. Likewise, they would have to slow down at a rate where inertia does not kill the humans or put them under unnatural forces. Ideally, both acceleration and deceleration would be at ideal rates to cause inertia forces to match the gravitation humans are used to on Earth. By you calculations, you use up almost two years in acceleration and deceleration. Alpha Centari is 4.367 light years away. You add two more years for the inertia effects.