Does the brake system have to be flushed and bleed after installing a new power booster? I didn't see it mentioned in the hayne's manual. Car seems to be performing phenomenally better than before.

 

Flushing, no, unless your fluid is really old and you wanted to for preventive maintenance.

I haven't needed to replace my booster yet, so no personal experience. But seems that bleeding would only be required if air was introduced in the system. And if you're already back on the road and brakes are working great, you're probably OK. If you had air in the lines, it would generally be apparent pretty quick.