Following is a response from DHS staff member, Tom Pullum:
I will paste below Stata lines that DO give the 19.6% for the Malawi 2004 survey, with additional lines showing how to get separate percentages treated for children having fever or having cough (ARI symptoms). I suspect that your issue was in how to distinguish between NA and 0 for the joint indicator of fever or cough, i.e. fever and/or cough. I have not tested this for the Rwanda survey. Please let me know if you still have questions.
* Match table 9.16 in Malawi 2004 report
use "C:\Users\26216\ICF\Analysis - Shared Resources\Data\DHSdata\MWKR4EFL.DTA", clear
gen wt=v005/1000000
* Construct binary outcome for had fever
gen fever=0 if h22<.
replace fever=1 if h22==1
tab fever [iweight=wt],m
* Matches 18.8%
* Construct binary outcome for had cough
gen cough=0 if h31<.
replace cough=1 if h31b==1
tab cough [iweight=wt]
* Matches 37.1%
* Construct binary outcome for had fever or cough
gen fever_cough=0 if fever<. & cough<.
replace fever_cough=1 if fever==1 | cough==1
tab fever_cough [iweight=wt]
* Construct binary outcome for whether had medical treatment,
* given had fever or cough
gen treatment_for_fever_cough=0 if fever_cough==1
replace treatment_for_fever_cough=1 if fever_cough==1 & h32z==1
tab treatment_for_fever_cough [iweight=wt]
* Matches 19.6% and 4360
* Extend to separate binary outcomes for whether had medical treatment,
* given had fever OR given cough
gen treatment_for_fever=0 if fever==1
replace treatment_for_fever=1 if fever==1 & h32z==1
tab treatment_for_fever [iweight=wt]
* Gives 15.9%
gen treatment_for_cough=0 if cough==1
replace treatment_for_cough=1 if cough==1 & h32z==1
tab treatment_for_cough [iweight=wt]
* Gives 36.5%