Is there any halachic basis to not putting on 2 pieces of clothing at the same time? As example, can one put on a jacket and outer coat simultaneously. (The jacket is already inside the outer cat)

Shalom, The law about putting on two garments at the same time can be found in the Kitzur Shulchan Aruch (R' Ganzfried) Chapter 3,5. The earlier source is from the Magen Avraham (Orach Haim 2, 3) who quotes it from the kabalistic sources, and explains that it could result in forgetfulness. This is not an absolute law, and appears in the Shulchan Aruch of the [Chabad] Rav as "It is good not to don two items at once", and in the Magen Avraham as "One should be careful..." (not "it is forbidden..."). In any event, if the jacket is designed to be a lining for the coat, it would certainly be considered as one item, even though they could be worn as separate items also. Blessings, D. Sperling.