The Halquas in the Mamluk army could be classified as flexible cavalry since there were several Mongols among them or at least a part as an upgrade of a part of them.
The Mongols who entered Mamluk service (some were even recruited into the Bahriyya IIRC) were incorporated as essentially normal mamluks individually rather than as a cohesive ethnic body and do not appear to have fought in the "native" manner or affected how the Mamluk army fought. I don't think there is any basis for Flexibles based on this.
This is different from the Mongols who entered the service of the Delhi sultanate FWIW where they did operate separately - I posted a list suggestion on this a bit back.