how viscous is the fluid in our ears?

That fluid is called endolymph.
You can look at the table on page 496 of the source below and see values (in units of centipoise) that have been measured for the viscosity of endolymph.  (The symbol used for the viscosity there is "η", the Greek letter eta.)

As a practical matter, I would expect the viscosity of endolymph to be relatively low, since it must respond quickly as we change the positions of our heads.  Something viscous like molasses would make bad endolymph.

(As another practical matter, this is not a question so much about Chemistry.  You'd likely get more answers by moving it to Medicine or Biology.)