I just recently removed a pine tree from my yard. I'd like to know if there is a flowering shrub that can be planted in that spot?

Sure, how much sun does the area get now? What characteristics are you looking for in a shrub - evergreen, flowering, scent, height, width ....?

Digging through tree roots to prepare the soil to receive a shrub may prove challenging. Pine trees thrive in acidic soil, so you will need an acid-loving shrub. As indicated, light conditions are a consideration. Too, size at maturity and care and maintenance, disease resistance, drought tolerance are considerations. And, you will want a shrub that is recommended for your growing zone.