I have a question regarding the vowels on Tafkheem letters.

Assalaamu Alaikum

I have a question regarding the vowels on Tafkheem letters.

In reply to an earlier question, you had stated that "the vowels on the tafkheem letter also have tafkheem and this is a very good question.  The sound of a voweled letter comes out with the vowel, so the vowel must have all of the characteristics that the letter has, otherwise it will not have the true sound required.  This is most notable when a letter has a shaddah on it."

My question is, how would we pronounce "mustaqeem" (surah Fatihah). Thinking of the yaa madda ('ee' sound) as two kasrahs combined together, then going by the above rule, would we pronounce the "first kasrah" with tafkheem and "second kasrah" with tarqeeq?

Best Regards

Wa alaikum assalaam wa rahmatullahi wa barakatuh,
The kasrah on the qaaf in the word al- mustaqeem would be read with the same level of tafkheem as the the qaaf, and the ya' meddiyyah, or the ya' saakinah would not be read with tafkheem and instead it would be read with tarqeeq.  It is another letter than the vowel on the qaaf, even though the kasrah is required for it to be a medd letter, it is not influenced by the tafkheem letter preceding it. 
May Allah grant you all khair.