Prepare for manually removing the creeping Charlie by watering the area deeply one to two days before you attempt to remove the unwanted plants by hand as this will ease removal of the plant with roots intact. Do this in the early spring just before or just as the creeping Charlie is starting to produce its blue flowers. Proper timing will help to prevent another season of self-seeding after bloom, which will exacerbate the infestation.
Don a pair of garden gloves and grasp the creeping Charlie plant clumps under the leaves at their base just at the soil line. Get a good grip with your entire hand surface and pull the entire clump up and out of the soil with a firm yank. Repeat for all the large central clumps interspersed between your creeping phlox plants and then go back for smaller tendrils still remaining in the soil.
Drop each removed clump immediately in a trash bag or waste can to prevent the plant pieces from being lost and rerooting or seeding themselves in and among the phlox.
Repeat this process several times during the year, as needed, to fully eradicate the species in your phlox bed.
Mulch over the soil where you have manually removed the creeping Charlie, in between the phlox plants, with a few inches of shredded bark or cocoa bean hulls or similar mulch. This will help to smother any latent creeping Charlie roots and keep weed regrowth down but not hinder the growth of the phlox.
Prune back overhead shrubs and trees that may be shading the area where creeping Charlie has invaded the phlox. Creeping Charlie prefers shade conditions and creeping phlox prefers full sun. By changing the sun exposure, you will weaken the growth rate of the creeping Charlie and boost the growth rate of the creeping phlox.