What is the relation between chemical thermodynamics and chemical kinetics? Can one be understood on the basis of the other or are they not interrelated at all?

The first thing my kinetics textbook demonstrated was how thermodynamics ignores time taken for a process whereas kinetics considers the time and rate of the process and hence kinetics is a more effective way to view change.

Also, I saw examples of highly thermodynamically feasible reactions which were not kinetically favourable in the sense that they were so slow that the entire process could be neglected as not happening.

Can one understand the thermodynamics of a reaction by studying it kinetics?

Or can one figure out the kinetics of a reaction by thermodynamical consideration?

Also, would it be a wise observation to say that thermodynamics is a largely theoretical subject while kinetics is a more experimental field?
No. Both I think are equally theoritical or experimental. You must study both seperately. Thermodynamics doesn't speak about rates. While kinetics doesn't tell you stability. 
If a reaction produces more than one product, thermodynamics will tell you which is more stable, while that doesn't necessarily mean it is the major product. It may happen that rate of formation of other product is more under certain conditionds. Read about thermodynamic vs kinetic product and you will get it.