Will a letter of recommendation from a postdoc fellow be valued for applying a PhD program?
What the admission committee looks for is specific and reliable information about the skills of the applicant.


Specific. If a postdoc fellow, or any other member of a team worked with you long enough, they usually can describe in some details what you achieved and how your skills and mindset helped you to achieve this. The more specific examples they could provide usually the better. In academic reality sometimes students spend more time with their TA's than their Profs, and I think people in admissions usually realise that. 
Reliable The letters from Profs are usually considered as more reliable than the letters from colleagues of moderate rank, and not without a reason. Indeed, if a Prof would decide to praise his student more than they deserve, it would be noted, remembered and all further letters from him would be taken with a bit of salt. Therefore, Profs are really responsible for providing actual information to each other in a small world of academia. RAs and TAs do not necessarily feel that their academic credibility is at stake, and can be more inclined to "help" the student by over-assessing their abilities and achievements in their reference. 


The balance of these two factors makes the game. My suggestion is --- go and ask that postdoc to write a reference for you, but also ask them to be very specific about everything they write, and only put in their letter the information which can be justified by some evidence.