Battery state of health (SOH) estimation is one of the three main analytical tasks of a battery management system (BMS), when viewed from engineering maintenance and prognostics perspective. With the current global effort towards more suitable and greener processes, lithium-ion batteries have shown to be an important element in facilitating this transition. One industry where this can be noticed in particular is the transportation sector, where a strong shift towards battery electric vehicles (BEV) can be observed. Within the aviation sector, current research efforts include electrical flight. However, numerous challenges remain, that are typically observable within a safety critical domain such as aerospace. One these challenges includes the determination of uncertainty in battery SOH prediction. This would provide improved transparency on the capabilities and limitation of a model, when used as part of a battery system. Within this report we propose the use of a bidirectional gated recurrent unit (Bi-GRU) with learnable soft attention, to predict battery SOH based on charge measurements. Uncertainty analysis is enabled through the use of simultaneous quantile regression (SQR) and orthonormal certificate (OC), to be able to highlight and distinguish the aleatoric and epistemic uncertainty of the proposed model. We afterwards evaluate the model for point prediction accuracy using standard metrics, and evaluate the produced uncertainty using specialised test cases and calibration metrics. We achieved strong results using the proposed framework on a 2-phase fast charging dataset published by Toyota.