I keep coming back to this post. The idea of having loose furniture in a MH just bothers me.
I agree with the other responders. In normal use the chair will not move. However, what happens in an emergency, either from hard braking or slamming into an immovable object? I would hate to survive the stop only to have my neck broken by my flying recliner.
Bolt the chair down.
My Winnebago uses a bracket/clamp and a large knob-screw to hold the recliner down during travel. Go to a dealer and take a look at one. The hardware could be order from Winnebagooutdoor.com.
Woodworker Supply sells a three wing T nut that could be screwed into the floor - Woodworker.com: CAST ZINC THREE WING TEE NUTS