Similar indices in MS SQL Server
The indexes are similar but not identical. The order of the columns in an index matters - a lot - and affects what queries might benefit from them.

We don't know your queries but for example a query like the following would benefit most from index A:

SELECT TOP (3) ChannelSKUID, Checked, SalesRank
FROM dbo.SalesRankCheck
WHERE ChannelSKUID = 'XXX'
ORDER BY Checked ;


while this one would benefit from index B:

SELECT TOP (3) ChannelSKUID, Checked, SalesRank
FROM dbo.SalesRankCheck
WHERE SalesRank = 1 
ORDER BY Checked ;


If only one of the two indexes were available, the query plans might still use it but the plan would not be optimal, due to the difference in column order in the index and the mismatch with the optimal column order needed for the query. The index would still be "covering" the query but the plan would probably be a full index scan instead of an index seek and would have additional (sort) operations as the rows provided by the index would not be in the order the query wants. 



For the question now:


  Am I right in thinking that this isn't a sensible way of having it organised and it would make more sense to have a single index with all 3 columns indexed or does that depend on the way the database is being used?


No, it is a sensible way and I wouldn't expect a single index to cover queries that might choose either index otherwise.  

But it depends on what queries run against the table. Any analysis should be based on the workload you have and the performance you expect. Analyze the queries (all of them or the ones most often run) and what indexes they use and what performance you get, before you decide dropping or adding an index. 

Run tests in test installations with different indexing, if performance is not good. Or experiment (say with dropping an index), if you think that the index is not used. 

For a quick and dirty advice, if the number of indexes on the table is small and the performance is good, don't bother changing anything. The extra load that indexes impose on write operations is usually small, unless you have a table with 10+ indexes or a table that is under extreme write load (thousands of writes per second).