-Have two max stat dwellers breed.
-When they have a baby there is a chance to have that baby be legendary or rare.
-There will be a 13.3%~ chance for the baby to be rare (28 special total)
-More importantly, there is a 6.6%~ chance to have a legendary baby (40 special stat total.)
-Remember it takes patience because it is roughly 1/20 chance to get a legendary baby.

Link to the Reddit post.
Children have a small chance of being born either rare (28 S.P.E.C.I.A.L) or legendary (40 S.P.E.C.I.A.L) if the parents' total S.P.E.C.I.A.L is high enough.
S.P.E.C.I.A.L-boosting gear does not affect this calculation.
Children have a 50/50 chance of inheriting the "proficiency" (highest stat) of either parent.
Maxed parents' proficiency is always Intelligence. (source1) (source2) (proof)

Child stats appear to be calculated at the time of birth. There is a special case to handle "ghost dads" which always results in normal children who inherit from the mother, though it is not clear whether it's actually used or is just an edge case error handler.

"Super" Child Formula

max = (male_total_special + female_total_special - 14) / 126
random_number = random(max / 4, max)
if random_number is greater than 0.95 the child will be legendary
if random_number is greater than 0.85 the child will be rare
otherwise the child will be normal

Notes:

• Parents' total S.P.E.C.I.A.L must be 134 or higher to have a chance at a legendary child.
  
• Parents' total S.P.E.C.I.A.L must be 122 or higher to have a chance at a rare child.
  
• Two fully maxed out parents (S.P.E.C.I.A.L 140) will have a ~6.6% chance of producing a legendary
• child, and a ~13.3% chance of producing a rare child.
  
• Two maxed parents will produce a child with an Intelligence proficiency.

Stat Distribution Formula

There are five starting input variables that presumably change according to legendary/rare/normal status (unfortunately, I have not been able to find that information):

• minimum_maxed_specials (default: 0)
  
• maximum_maxed_specials (default: 1)
  
• max_special_value (default: 8)
  
• maxed_special_stats (a list of S.P.E.C.I.A.L stats that will be maxed, default: "proficiency" stat
• inherited from parent)
  
• total_point_pool (default: 38)

When stats are assigned, two new input variables are calculated:
maxed_special_stats_count = random(minimum_maxed_specials, maximum_maxed_specials + 1) (by default this value will be between 0 and 2)
total_stat_points = total_point_pool - 7 (by default this value will be 31)

Distribution Process:

• Step 1: maxed_special_stats are looped and assigned a level of max_special_value. For each iteration, max_special_stats_count is decreased by 1, and total_stat_points is decreased by (max_special_value - 1). All S.P.E.C.I.A.L stats assigned during this step are removed from the rest of the calculation.
  
  
• Step 2: maxed_special_stats_count is looped. For each iteration, a random stat is chosen from the remaining available SPECIAL and is assigned a level of max_special_value. total_stat_points is decreased by (max_special_value - 1). All S.P.E.C.I.A.L stats assigned during this step are removed from the rest of the calculation.
  
  
• Step 3: All remaining unassigned S.P.E.C.I.A.L stats are looped and assigned a value of 1. For each iteration, total_stat_points is decreased by 1.
  
  
• Step 4: total_stat_points is looped. For each iteration, a random stat is chosen and its level is increased by 1. If its value is greater than or equal to (max_special_value - 1), that S.P.E.C.I.A.L stat is removed from the loop. Loop continues until all of total_stat_points are assigned.
  That's all the info I have for now; I'm continuing to look for the hard numbers regarding legendary, rare, and normal dweller stats. I assume even normal dwellers have a different set of input variables than the default since they do not receive any S.P.E.C.I.A.L stats with a level of 8.
  I will do my best to answer any questions about dweller inheritance (or anything else my crystal ball is able to tell me about game mechanics; please keep in mind it can be hard to read).

Two max S.P.E.C.I.A.L parents have a 6% chance of producing a child with 40 S.P.E.C.I.A.L and a 13% chance of producing a child with 28 SPECIAL (as opposed to the normal 12). Kids have a 50/50 chance of inheriting either parent's highest skill. Gear does not affect odds.