  Long coherence times, large anharmonicity and robust charge-noise
insensitivity render fluxonium qubits an interesting alternative to transmons.
Recent experiments have demonstrated record coherence times for low-frequency
fluxonia. Here, we propose a galvanic-coupling scheme with flux-tunable
$\textit{XX}$ coupling. To implement a high-fidelity entangling
$\sqrt{i\mathrm{SWAP}}$ gate, we modulate the strength of this coupling and
devise variable-time identity gates to synchronize required single-qubit
operations. Both types of gates are implemented using strong ac flux drives,
lasting for only a few drive periods. We employ a theoretical framework capable
of capturing qubit dynamics beyond the rotating-wave approximation (RWA) as
required for such strong drives. We predict an open-system fidelity of
$F>0.999$ for the $\sqrt{i\mathrm{SWAP}}$ gate under realistic conditions.
