You can initiate a read cycle every Clk cycle if you want to perform back to back reads. You can also verify this in the datasheet on page 26, Figure 7, where we have shown one instance of consecutive reads.
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After the initial delay, you can read data at every clock cycle. Refer the timing diagram "Figure 7. Read/Write Cycle Timing" on page 26 of the datasheet (http://www.cypress.com/file/226446/download ). Please check how data from locations 'A1' and 'A2' are read out.