To quantitatively assess target and organs-at-risk (OAR) dose rate based on three proposed proton PBS dose rate metrics and study FLASH intensity-modulated proton therapy (IMPT) treatment planning using transmission beams. An in-house FLASH planning platform was developed to optimize transmission (shoot-through) plans for nine consecutive lung cancer patients previously planned with proton SBRT. Dose and dose rate calculation codes were developed to quantify three types of dose rate calculation methods (dose-averaged dose rate (DADR), average dose rate (ADR), and dose-threshold dose rate (DTDR)) based on both phantom and patient treatment plans. Two different minimum MU/spot settings were used to optimize two different dose regimes, 34-Gy in one fraction and 45-Gy in three fractions. The OAR sparing and target coverage can be optimized with good uniformity (hotspot < 110% of prescription dose). ADR, accounting for the spot dwelling and scanning time, gives the lowest dose rate; DTDR, not considering this time but a dose-threshold, gives an intermediate dose rate, whereas DADR gives the highest dose rate without considering any time or dose-threshold. All three dose rates attenuate along the beam direction, and the highest dose rate regions often occur on the field edge for ADR and DTDR, whereas DADR has a better dose rate uniformity. The differences in dose rate metrics have led a large variation for OARs dose rate assessment, posing challenges to FLASH clinical implementation. This is the first attempt to study the impact of the dose rate models, and more investigations and evidence for the details of proton PBS FLASH parameters are needed to explore the correlation between FLASH efficacy and the dose rate metrics.