Rheumatic heart disease (RHD) remains a major public health concern across low- and middle-income countries in the Global South. Early detection through community-based screening of asymptomatic individuals has been identified as a critical strategy for reducing the disease burden. Despite this, the absence of accessible, automated population screening tools continues to impede implementation at scale. This study investigates the screening potential of integrating electrocardiography (ECG) and phonocardiography (PCG) for the early detection of RHD in asymptomatic schoolchildren. The dataset was obtained as part of an ambulatory screening initiative conducted across multiple school sites in rural areas of Ethiopia. It comprised ECG and PCG recordings from 611 asymptomatic schoolchildren aged 10 to 20 years. A comprehensive set of time-frequency, visibility graph and non-linear features were extracted from both signal modalities. These features were subsequently evaluated using machine learning models to assess their utility in the automated screening of early RHD. The best model achieved an average 10-folds cross-validation scores on sensitivity, positive-predictive-value and F1-score of 59.6%, 63.6% and 60.8%, respectively for multimodal ECG and PCG signals. Whereas separate evaluation of ECG showed an F1-score of 61.1% and PCG achieved 23.5%. Key features included the T-wave, the area under the QRS complex, and entropy measures derived from beat visibility graphs in the ECG. In addition, visibility graph features from multi-band S1 and S2 heart sound segments, along with MFCC coefficients from the PCG, were also relevant. However, PCG alone performed poorly and did not show improved results over the ECG features. Although auscultation is key clinical diagnosis tool in symptomatic RHD, combined PCG with ECG features does not enhance asymptomatic RHD detection using the ECG modality alone.