Flypool shows the shares you submitted for the current round. They use the Pay Per Last N Shares (PPLNS) algorithm in their pool. Basically, shares from the previous round(s) are included when determining work done this round to stop pool hoppers from messing up the pool. But they don’t show “total shares submitted since you started mining”. Each round/block - every several minutes at the moment - it goes back to zero for the new round.
They also display “effective” hashrate and average “effective” hashrate. Over 24 hours or so, you should see your effective average hashrate come in line with what your miner says locally - ± a few hashes since it bases it off of conditions of the network and your submitted shares to estimate your actual hashrate. If you see that your current hashrate is not the same as locally that is because it fluctuates based on number of shares you submit each round. If after 24 hours your effective average hashrate is way off you may have a problem.
Hope that helps.