Yes you can get a Quilava with both Double Kick and Extrasensory but your Quilava cannot be taught them. Therefore to get a Quilava will both Double Kick and Extrasensory you will have to breed yours.
To get Double Kick put your Quilava in the Day Care Centre with either a Nidoran♂, Nidorino, Nidoking, Jolteon, Combusken, Blaziken, Deerling or Sawsbuck that already has the Move Double Kick. After you have put them in the Day Care Centre run around for a while until the Day Care Man calls you over to give you an egg. Then run around again until the egg hatches. When the egg does finally hatch the Cyndaquil that just hatched from it should have the Move Double Kick.
To get Extrasensory put the hatched Cyndaquil straight back into the Day Care Centre but this time put it in with either a Vulpix, Ninetales, Nuzleaf or Shiftry that already has the Move Extrasensory. Then repeat the same process as you did before and run around for a bit until the Day Care Man calls you over to give you another egg. Then run around again until this egg hatches, when it does finally hatch the Cyndaquil that just hatched from it should have both Double Kick and Extrasensory.
Hope I helped :)