If your burst is 3 beat max, then the depth should be 3 isnt it? Provided the 3 data is read out before a new burst come in. Otherwise you need to do some math, or use handshake signals to delay input burst.
Upon finishing 2nd beat, the first beat is read out completely, thus 2 data is needed, but the design is more compicated.
It also depends on over a time period how many 16b unit is accumulated in the FIFO since the read out is slower than input.