This is probably not connected to your Phillip, but just in case (since one never knows) We have a Phillip B. Johnston born Virginia to Stephen Johnston (1721-d. bef. 1801) who married in Essex Co., VA to Phoebe Samuel, dau. of Henry Samuel. Stephen Johnston was son of William Buford Johnston (abt 1680 - 1728) who married (possibly secondly) to Mary Goodloe (abt 1699 -1732/3) in Middlesex Co., VA.

Phillip B. Johnston married an Elizabeth (surname unknown) and they went to Kentucky where Phillip died in Shelby Co., KY 1821. One source I found said "without issue", so that is why I say this may not be your Phillip's line; but...maybe that source was only unable to find any issue.
Phillip B. Johns(t)on witnessed a couple of land sales for his father in 1782 and 1789 in Spotsylvania Co., VA.
Phillip (middle name not know, but may have been Bufurd or Byrd) Johnston was only son of Stephen and had sisters named: Clara, Frances, Sarah, Mary and Catherine.
Stephen Johnston (and his brother Henry) were both carpenters.
If this does connect to your line, I have more on the sisters, etc. that I will gladly share.