Experiments with a flue showed the incense burns in an updraft but there's no backflow.  The trick is getting rid of the updraft in the section where the backflow is needed.  Making more holes in the flue still doesn't get it to backflow.  As long as there's a hole in the base, there's an updraft.

Encasing the stand gets somewhat of a pool to form at the base but the updraft returns as soon as this is enclosed in a cylinder, no matter how many holes are in it.  The rocket would have to be 2 parts made of metal & the hot part would have to be integrated in the base.  The backflow area needs an air seal from the updraft area.

It goes back to integrating the hot part in a plastic model of the base.  Maybe a big old block of clay could be stuffed between the bottom of the metal stand & the rocket's cylinder to form a heat resistant air seal.  The stand needs be tall enough to not transfer too much heat to the clay, which transfers heat to the PLA.  The only reason for using clay is it transfers heat more slowly than metal.  Of course a tall enough, 4 sided metal stand might be safe to attach directly to PLA through farsteners.

This thing evolved.

It made a pretty convincing rocket exhaust pool when placed over a dark surface.  It should be in a tub to make a deeper pool.

At this point, the metal part could be held down just by gravity so it could be taken off easily.  The PLA should rise above the clay for attaching the nose cone/wind break.  The clay is stiff enough to shape without any top or bottom forms.  The clay should be as low as possible to make it bottom heavy.  The rocket needs a 44mm diameter to clear the square metal stand.  A round stand might get away with 30mm.

Masking tape seemed to be good enough to work around the limited metal fabrication. 

https://www.amazon.com/Backflow-Incense-Holder-Fragrance-Accessories/dp/B0B2HTRZ8S

There are super expensive metal funnels which could to the job.  They might burn the clay.  Another idea is to JB weld a metal pipe to a metal bowl but JB weld can't withstand the heat.  What a lion would do for a TIG welder.

https://www.walmart.com/ip/Better-Homes-Gardens-Black-Wood-Glass-Backflow-Incense-Burner-Kit/1874162989

An off the shelf system just has the backflow part & a pool enclosed.  It has a large thermal mass holding the cone but still has a glass window.  While it could have a starship go over the cone & the smoke appearing to exit, it would melt the PLA & there would still be a large black piece between the rocket & the exhaust. 

Fully enclosing the exhaust part of the lion design would create a big division between the exhaust part & the rocket part.  It would be a transparent pedestal the rocket sat on.