I would also recommend using D86 (which comes with A86) as it lets you type in 8086 instructions interactively so you can see what happens to all the registers and flags after each instruction.
This code (as other have pointed out):
MOV AL, F2h
ADD AL, 20h
will only affect the flags and the AL register. No other eight-bit register will be affected (even AH). AX will change though since it is made up of AH and AL, so if AH was 42h:
Code AL AH AX
MOV AL,F2h F2 42 42f2
ADD AL,20h 12 42 4212
The result of that particular operation will set the carry flag and the parity flag and clear the overflow, zero, sign and auxillary carry flags.
You may think that the overflow flag should be set, but the overflow flag treats the values as signed values (in this case -14 and 32) and the addition doesn't exceed the maximum signed value (127). The carry flag treats the values as unsigned values (242 and 32) and the addition exceeds the maximum unsigned value: 242 + 32 = 274 which is greater than 255 so the carry is set.