Flexible air bladders and associated air assemblies provide compression and blood flow moderation in a variety of applications including blood flow restriction training (BFR) and limb compression for injury prevention. An integrated air assembly comprises a flexible manual pump, a check valve air intake, one-way valve and a pressure release valve. The user can properly position and fasten the air bladder around a limb using a special type of band, sleeve, or by wearing a piece of clothing containing strategically placed air bladders and integrated air assemblies. Each air assembly allows the user to easily and manually add air to the bladder by pressing on a designated area of the pump which causes the bladder to extend on the inward facing portion of the band, compression sleeve, or piece of clothing toward the limb until a desired pressure is achieved around the limb to support blood flow moderation.