The coupling of electricity and gas systems has been ever-augmented with the wide deployment of gas-fired generators, which facilitates the conception of the integrated electricity and gas system (IEGS). Probabilistic energy flow (PEF) analysis is usually conducted to assess the operating status of the IEGS by calculating the probability distribution of state variables (e.g., gas pressure, gas flow, voltage, and power flow). However, multiform time-variant uncertainties can simultaneously reside in the IEGS, including discrete (e.g., the component failure or functioning) and continuous ones (e.g., renewable energy outputs). Existing PEF analysis works cannot completely deal with time-variant multiform uncertainties featured with different mathematical characteristics. This limitation hinders the estimation of potential operating risks of the IEGS. To address this, this paper proposes a generalized framework for analyzing the probabilistic energy flow of the IEGS considering multiform uncertainties. Firstly, both time-varying random working states and variable outputs of components are represented as probabilistic models utilizing the L- transform technique. The probabilistic model is composed of some representative states depicting possible realizations of the component's performance and corresponding probabilities. On this basis, the optimal energy flow (OEF) operator is defined to aggregate probabilistic models of different components to determine probabilistic models of energy flows in the IEGS. Furthermore, multidimensional indices are constructed to comprehensively explore the probabilistic features of energy flows and the impact of probabilistic energy flows on the system performance. In this paper, the system performance mainly refers to the energy-serving capability of the IEGS. Specifically, probabilistic distribution characteristics of energy flows are explicitly displayed by relevant expectations, standard deviations as well as skewnesses. Indices such as the nodal expected gas and electricity not supplied are adopted to evaluate the influence of the probabilistic energy flow on the system performance. Numerical studies reveal that energy flows through different pipelines or power lines present diversified statistical characteristics, which indicates that they are influenced by multiform uncertainties to different extents.