If possible I would prefer to start from the commercially available 16-bromo derivates

In palmitic acid first you can protect the acid group then base catalyst can be used to remove the proton from the methyl group the HBr can be used it is useful for bromo derivative and finally hydrolysis to form 16- Hydroxypalmitic acid. 

Selective bromination of palmitic acid or its ester derivative using reagents such as N-bromosuccinimide (NBS) will give you 16-bromopalmitic acid. Bromoderivative can be transformed into hydroxyl derivative by using NaOH or KOH as base.

1- Add 1,6-dicyanohexane (1 eq)   to 4-actetoxybutyl magnesium bromide (1 eq) in THF and stir for 2 hr at room temp.(N.B. Protect from moisure by CaCl2 tube). After two hours pour the prepared product onto a Grignard reagent from ethyl 4-bromobutanoate and complete stirring for further two hours. Addition of water and extraction will provide 16-acetoxy-4,11-dioxohexadecanoate as ethyl ester.   

2- Hydrolize the ester and the acetoxy- to obtain 16-hydroxy-4,11-dioxohexadecanoic acid. Then follow Climmensen reduction 

http://en.wikipedia.org/wiki/Clemmensen_reduction

I hope it works for the synthesis of 16-hydroxy.derivative

The isomer 15-hydroxy can be obtained from 16-hydroxy- after dehydration followed by oxymercuration-demecuration 

Good luck

Your question has already been answered above by experts in this reaction. Alternatively, its available from commercial source. It would be better to buy it unless you want in large excess.

Thank you for your suggestions 

but ,I want to synthesis 16-hydroxy palmitic or 15-hydroxy palmitic by using palmitic acid as starting material.

If you want to use palmitic acid then enzymatic oxidation would be the way to go.

There are a few patents and publications on this already

PCT Int. Appl., 2006105082, 05 Oct 2006

U.S. Pat. Appl. Publ., 20080057577, 06 Mar 2008

Journal of General Microbiology, 128(5), 1125-34; 1982

For a synthetic method you could try utilising the reactivity of Schwartz's reagent. It would require dehydrogenating at the alpha position of the acid, appropriately protecting the free acid, then using Schwartz's reagent to isomerise to the omega position and work up with hydrogen peroxide.

Aleuritic acid is available commercially. Try converting it.