We study the effect of magnetism and perpendicular external electric field strengths on the energy gap of length confined bilayer graphene nanoribbons (or nanoflakes) as a function of ribbon width and length using a first-principles density-functional electronic structure method and a semilocal exchange-correlation approximation. We assume $AB$ (Bernal) bilayer stacking and consider both armchair and zigzag edges, and for each edge type, we consider the two edge alignments, namely, $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ edge alignment. For the armchair nanoflakes we identify three distinct classes of bilayer energy gaps, determined by the number of carbon chains in the width direction ($N=3p$, $3p+1$ and $3p+2$, $p$ is an integer), and the gaps decrease with increasing width except for class $3p+2$ armchair nanoribbons. Metallic-like behavior seen in armchair bilayer nanoribbons are found to be absent in armchair nanoflakes. Class $3p+2$ armchair nanoflakes show significant length dependence. We find that the gaps decrease with the applied electric fields due to large intrinsic gap of the nanoflake. The existence of a critical gap with respect to the applied field, therefore, is not predicted by our calculations. Magnetism between the layers plays a major role in enhancing the gap values resulting from the geometrical confinement, hinting at an interplay of magnetism and geometrical confinement in finite size bilayer graphene.