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Flight delays in passenger air transportation systems may cause numerous troubles to people's daily life. Empirical works show that at the microscopic level there exist different kinds of inter-correlations, while at the macroscopic level the complex system obeys a simple law similar with that for gases. The constructed theoretical models are not consistent with each other, leading to some debates. How the macroscopic law emerges from the detailed cross-correlations is an open question. And an empirical benchmark to end the debates is also required. In the present work, the cosine correlations between airports for three kinds of flight delays are calculated, the relationships of which versus delay time can be re-scaled by the average number of flights H per month to a universal scaling relation, 〈 C o s θ λ 〉 H p = f λ (〈 T λ 〉 H q) , where p and q are exponents. Hence, the system can work in two kinds of critical phases, namely, the stable phases in the durations from 1995 to 2000 and from 2005 to 2019, and the transition phases in the durations from 2001 to 2004 and within the year 2020. The results provide an empirical benchmark for building models. • American domestic passenger flight records from 1995 to 2020 are downloaded. • Three kinds of cosine correlations and delay time are defined from data. • Scaling relations are obtained by rescaling flight number H per month. • The air transportation systems are confirmed to be in critical states. • Two stable phases and two transition phases are identified. [ABSTRACT FROM AUTHOR]