How many Blackjack sequences in that list?

Python 2, 215 bytes

def b(s,a=[],r=range):
 S=map(lambda x:":">x>"1"and int(x)or 10-(x=="A")*9,s)
 for i in r(12):
  for j in r(13):
   if 21in[x*10+sum(S[i:j])for x in r(S[i:j].count(1)+1)]and s[i:j]not in a:a+=s[i:j],
 return len(a)

Comments added:

def b(s,a=[],r=range):                                      # Define the function b and a list, a, which holds all the blackjack sequences
 S=map(lambda x:":">x>"1"and int(x)or 10-(x=="A")*9,s)      # Set S to the score of each card in b
 for i in r(12):                                            # Loop with i from 0 to 11
  for j in r(13):                                           # Loop with j from 0 to 12
   if 21in[x*10+sum(S[i:j])for x in r(S[i:j].count(1)+1)]\  # If 21 is included in all the possible sums that the scores between i and j in S can be
           and s[i:j]not in a:                              # And that sequence is not already included,
               a+=s[i:j],                                   # Append that sequence to a
 return len(a)                                              # Return the amount of elements in a

Jelly, 30 29 bytes

1e×5,⁵Ḥ‘
O_48«26%⁴µSeÇ
ẆÇÐfQL

Try It Online! or check out the test suite

How?

Note that, if we always value an ace as 1 then the only valid sums are 21 and 11, the latter being acceptable iff an ace appears in the sequence.

ẆÇÐfQL - Main link: string
Ẇ      - all non-empty contiguous sublists
  Ðf   - filter keep if...
 Ç     -     last link (2) as a monad ...is truthy
    Q  - unique results
     L - length

O_48«26%⁴µSeÇ - Link 2, isBlackjackSubtring: char array  e.g. ['A','2','8','Q']
O             - cast to ordinal values                        [ 65, 50, 56, 81]
 _48          - subtract 48                                   [ 17,  2,  8, 33]
     26       - 26
    «         - minimum (vectorises)                          [ 17,  2,  8, 26]
        ⁴     - 16
       %      - modulo                                        [  1,  2,  8, 10]
         µ    - monadic chain separation (call the result v)
          S   - sum(v)                                        21
            Ç - last link (1) as a monad link_1(v)            [11,21]
           e  - exists in?                                    1

1e×5,⁵Ḥ‘ - Link 1 validSums: value list (where A is 1, and {T,J,Q,K} are 10)
1e       - 1 exists in? (are there any aces? Yields 1 or 0)
  ×5     - multiply by 5 (5 or 0)
     ⁵   - 10
    ,    - pair ([5,10] or [0,10])
      Ḥ  - double ([10,20] or [0,20])
       ‘ - increment ([11,21] or [1,21])
         -                        ^
         -     note: if no ace is in the sequence it's sum can't be 1 anyway

JavaScript (ES6), 144 138 129 128 126 124 bytes

g=([c,...s],a=[],q=new Set)=>c?g(s,[...a,[,21]].map(([x,y,A])=>[x+=c,y-=+c||(c<'B'?A=1:10),A,y&&y^10*A||q.add(x)]),q):q.size

Old attempt at 128:

s=>(q=new Set,f=s=>s?f(s.slice(1))&f(s.slice(0,-1))&[...s].map(c=>t+=-c||~(c<'B'?A=0:9),t=A=21)|t&&t-10*!A?q:q.add(s):q)(s).size