Reciprocity-based, joint coherent downlink beamforming from multiple access points (APs) in distributed multiple-input multiple-output (MIMO) with independent local oscillators (LOs) requires the APs to be periodically phase-calibrated (a.k.a. phase-synchronized or phase-aligned). Such phase calibration can be accomplished by bidirectional over-the-air measurements between the APs. In this paper, we show how such over-the-air measurements can be integrated into the time-division duplexing (TDD) flow by appropriately shifting the uplink/downlink switching points of the TDD slot structure, creating short time segments during which APs can measure on one another. We also show how this technique scales to large networks. Furthermore, we analytically characterize the tradeoff between the amount of resources spent on calibration measurements and the resulting spectral efficiency of the system, when conjugate beamforming or zero-forcing beamforming is used. The results demonstrate the feasibility of distributed MIMO with phase-calibration through over-the-air inter-AP measurements integrated into the TDD flow, and the advantage of this design over schemes with dedicated calibration slots.