Sunflowers are best grown in ground directly from seeds, they are fast growing plant and need fertilizers to produce big healthy blooms, they could be grown any time in Karachi, prepare the soil by mixing lots of ojhri ki khaad and water the soil for 1 week before planting seeds then level up the soil and sow seeds 6" apart.. water with care so the seeds dont get disturbed, they will germinate in 2-3 days, when the plants reach size of 12" support them with stakes, they are very tall plants and are easily knocked down by wind.. buy NPK granules from garden shops and start giving them every week 10-15 granules per plant taking care not to put the granules near the plant's stem or it will rot.. sunflowers die after flowering...
@ Farhan, rightly said the phlox is one of the most floriferous annual in our climate and grows without special care or fertilizers.. there is a good range of colors.. i grew these from paneeri and will be collecting the seeds color vise inshaAllah... the desi ones are self-sowing.. they germinate, grow and blooms in neglect, adding colors to the garden.. look at the self sowing phlox from last year:

Zinnias bloom through out the year in Karachi, the self sowing larkspurs in the picture have germinated too close to each other and i didnt thinned them out so they are short only 12"-16" in height, but those which are planted separately are now 30"-50" tall..
@ Umar: the maximum performance of petunias would be by March end inshaAllah..