When was the term Conflict of Interest first used and how was it
defined at the time?

Certainly by the early 1800s newspapers such as the London Times were
writing of the ?conflict of interest and passion? existing between two
parties of men or organisations. In these two issues of the Times the
phrase is used regarding the Irish problem.
The Times, Friday, Aug 20, 1819 
London, Monday, March 15, 1819 
Perhaps another researcher will be able to take it back further.
answerfinder-ga

I can't disagree with the above.
The concept is, of course, much, much older and common to all cultures
as the sayings in the box on p 3 of this site mentions:

http://www.gifa.org/Documents/Conflicts%20of%20Interest.pdf

It also (right column) mentions that it was a concept in Anglo-Saxon
fiduciary law.  The following from Etymonline is also related:

recuse Look up recuse at Dictionary.com
    1387, "to reject another's authority as prejudiced," from O.Fr.
recuser (13c.), from L. recusare "to refuse, make an objection," from
re- + causa (see cause). The word now is used mostly reflectively.

The last sentence refers to ideal situation that a person recuses
himself to avoid a conflict of interest.

But that doesn't give an earlier use of the expression itself.

Sources: http://dictionary.oed.com
Dictionary headword: 'conflict'
subheading: 'conflict of interest'
first attested use:
1837 Southern Lit. Messenger Dec. 752/1 My own convictions are that
our system of Federal Government, with virtue on the part of the
rulers, and vigilance on the part of the people, may exist forever.
Under a fair administration of its powers, no conflict of interest or
feeling can well arise.