If you have clearly cylinder, you could use PIV.

I would also recommend Particle Imaging Velocimetry, however it may be important to consider how the presence of tracer particles may influence the behavior of your film.

Another velocimetry technique that you may be interested in is Optical Coherence Tomography Velocimetry, which is described in the following paper.

https://www.researchgate.net/publication/265137770_Optical_Coherence_Tomography_Velocimetry_of_Colloidal_Suspensions

This is a very competitive technique as it has high spatial and temporal resolution, as well as the ability to measure opaque materials in real time. 

Article Optical Coherence Tomography Velocimetry of Colloidal Suspensions

You can send a message with your question (with more details (driving force, boundary condition, etc.) ) to my friends S.A.Chivilikhin, I.F.Melikhov (they are in ResearchGate) who deals with the Stokes flow of thin films (theoretical study).

Best wishes,

Igor Popov

Assuming everything is regular and you know enough about the fluid properties, there are analytical solutions for velocity in terms of the film thickness. It's ages since I've done this, but there's lots of literature (try Moffat, Stephen OBrien, S.K. Wilson, David Riley) out there about this - search for coating flows (outside the cylinder) or rimming flows (inside) or derive it from the Navier-Stokes equations & a thin-film approximation.

For a theoretical approach, people use long-wave assumptions to find the expressions of velocity, pressure and temperature and derive a long-wave model using it. The literature below  will give you a deep insight

1) http://www.utwente.nl/tnw/pcf/education/j.m.burgerscentrum_research_school_for_fluid_mechanics/jmbc_course_on_capillarity_driv/Articles/anton_darhuber/surface_tension_etc/Oron_RevModPhys97_thinFilms.pdf

2) http://www.coating.udel.edu/pdfs/obsch.pdf

3) http://link.springer.com/article/10.1007%2Fs10665-004-1772-7#page-1

4) http://www.aps.org/units/dfd/meetings/upload/Ashmore_DFD04.pdf

5) http://www.iscst.org/pages/ECSConf/ECS2007/Posters/Duffy_07.pdf

6) http://www.staff.ul.ie/eugenebenilov/hpage/pubs/jfm13b.pdf

You can also refer to work done as proposed by Joanne.

If you are doing experiments, I would recommend what Marcin and Alexander have proposed.