Cleaning old stone

Hi,
We have purchased a home built in the 60's that has a flagstone front hall and the kitchen is flagstone. We are remolding the kitchen and I thougt now would be a good time to make the floor look like new, but I can't find any info on the best way to do that. The flagsone is irregular and not flat. Obviously I wash it with soap and water weekly but it just doesn't wow me. There are some whiteish spots that don't come off and it must have at one time been sealed. Should we do this again and if so how do you remove all the years of build up? Or should we just leave it as is and not open anoother can of worms?

Thanks,in advance,for your help in this.

Best,
Christine