Future wireless cellular networks must support both enhanced mobile broadband (eMBB) and ultra-reliable low-latency communications (URLLC) to manage heterogeneous data traffic for emerging wireless services. To achieve this goal, a promising technique is to enable flexible frame structure by dynamically changing the data frame's numerology according to the channel information as well as traffic quality-of-service requirements. However, due to non-orthogonal subcarriers, this technique can result in an interference, known as inter numerology interference (INI), thus, degrading the network performance. In this work, a novel framework is proposed to analyze the INI in the uplink cellular communications. In particular, a closed-form expression is derived for the INI power in the uplink with a flexible frame structure and a new resource allocation problem is formulated to maximize the network spectral efficiency (SE) by jointly optimizing the power allocation and numerology selection in a multi-user uplink scenario. The simulation results validate the derived theoretical INI analyses and provide guidelines for the power allocation and numerology selection.