Is there something similar to creeping phlox that blooms throughout the season or close to?
rock cress - Aubrieta cultorum
None of the aubrietas will bloom for much longer than the phlox - all are considered to be mid to late spring bloomers.
FWIW, most perennial groundcovers will have a relatively limited bloom season - that is just the nature of perennials. They bloom for a couple weeks to a couple of months and then are done for the season. Annuals - with that biological urge to reproduce within the growing season - are generally the only plants with a season-long flowering period.
If you want a growing-season-long bloom period, you may have to consider a sequential assortment of flowering groundcovers. If you provide your location and sun conditions, perhaps we can get more specific.
And while it is not exactly considered a groundcover, the hardy geranium 'Rozanne' grows virtually throughout the US and in both sun and light shade and is recognized as having a very long bloom season. But it is more of a sprawling perennial than a true groundcover.
Here is a link that might be useful: Geranium Rozanne
Green & Gold (Chrysogonum virginianum) is one of the few long-blooming groundcovers though it hardly resembles phlox (yellow flowers) and it doesn't form a carpet of flowers like phlox. Blue Star Creeper (Isotoma fluviatilis) also produces (rather small) flowers for an extended period. Lithodora has a decent bloom period too -- spring into early summer. Plumbago resembles phlox but blooms late in the season so it makes a nice complement to creeping phlox.
Verbena Sissinghurst is the ticket! I planted this in my former Zone 6 garden and it was a reliable perennial and bloomer year after year. Drought tolerant too. You've got to like bright pink, however, because this variety comes only in pink.
There are numerous other varieties of ground cover verbena that come in other colors (in the blue, pink, red, white part of the rainbow) but in my experience, Sissinghurst is at the top of the list. No mildew, mites, etc. which I've encountered with other varieties.
Here is a link that might be useful: Verbena Sissinghurst