Yes you can install Vinyl siding over a brick chimney.
The outside of the chimney does not get hot so that the Vinyl siding does not melt and as long as you use the proper fasteners to install the vinyl siding onto the brick chimney it can be done.
You'll need to drill into the brick chimney and install those plastic anchors that the screw goes into so that the vinyl siding will stay on.
Make sure the chimney is in good condition and not falling apart when you install the vinyl siding on it otherwise the vinyl siding will also fall off.
I've seen people put vinyl siding on brick chimneys before and it worked out just great.