“Iron therapy induces inflammation, which could decrease iron absorption. Increased exposure of iron in the gut could also alter microbiome file.” 
“The statistical analysis revealed that the meal constituents which were found to influence iron absorption positively were ascorbic acid and β-carotene in breakfast and only β-carotene in dinner.” 
- Vitamin C capsules are unlikely to help
- Vitamin C from a citric fruit in the morning is desired.
- β-carotene should also be taken.
“In this setting, provision of iron-containing micronutrient powder MNPs to weaning infants adversely affects the gut microbiome, increasing pathogen abundance and causing intestinal inflammation.”
“Mothers of infants in the MNP + Fe group reported more infant days spent with cough (P = 0.003) and dyspnoea [shortness of breath] (P = 0.0002); “
“The present study suggests that in African children with a low enteropathogen burden, Fe status and dietary Fe supplementation did not significantly affect the dominant bacterial groups in the gut, faecal SCFA concentration or gut inflammation.” 
“The relative abundance of the genus Roseburia (phylum Firmicutes), a butyrate producer, increased in the Fe + Vitamin E group (Δ1.3%, P < 0.01). Also at the genus level, the genus Escherichia decreased by 1.2% on average among all participants (effect of time P = 0.01).” 
- So Iron Supplements reduces E.Coli, which is very low in CFS
“. Provision of iron fortificants to school-age children and iron-containing MNPs to weaning infants decreases the number of beneficial ‘barrier’ commensal gut bacteria (e.g., bifidobacteria), increases the enterobacteria to bifidobacteria ratio and abundances of opportunistic pathogens (e.g., pathogenic Escherichia coli), and induces gut inflammation. Thus, although iron-containing MNPs are highly effective in reducing IDA, they may increase gastrointestinal morbidity in infants, and safer formulations are needed.” 
“Consumption of rice fortified with micronutrients can increase hookworm prevalence, especially in environments with high infection pressure.” 
Without a proper control study done with CFS/IBS patients, I have reservations about doing any iron supplements. Eat a diet rich in natural iron instead (List). Have an orange and a slice of cantaloupe with breakfast always. See this list of beta-carotene food for supper.