You could have a function called fetch_id() that returns a record for a given id:

fetch_id <- function(id) { return(efetch(id, db=db, rettype = 'gp', retmode = retmode, retmax = returnAmount)); }

Then, given a vector of IDs:

ids <- c(124511, 124512, 124513, ... )

you can pre-allocate a list:

l <- vector(mode = "list", length = length(ids))

Then iterate over ids to populate the list l with fetched results:

l <- lapply(ids, function(id) { fetch_id(id); })

Once you have this list object populated, you can run lapply() on it to run a function of your choice on each element of it:

process_fetched_record <- function(fr) {
    rec <- gbRecord(fr)
    seq <- getSequence((ft(rec)))
    m <- as.data.frame(seq)
    setnames(m, "x", "sequence")
    protienName <- names(seq)
    m <- add_column(m, protienName, .after = 0)
    m$molecularweight <- mw(m$sequence)
    m$m<- str_count(m$sequence, 'm')
    m$cc <- str_count(m$sequence, 'cc')
    logvec <- grepl('(Protein)|(Region)', m$protienName)
    m <- subset(m, logvec)
    return(m)
}

m <- lapply(l, function(fr) { process_fetched_record(fr); })

Then you have a list m that you can access by index.

I'm not familiar with your code and I made a few adjustments to get it to run so hope it is still producing what you want...

But you asked for a loop that would iterate over your code without re-writing the output each time, hope this helps.

#Add list/data frame here (added test genes, also use 1:nrow(gene_list$gene) for data frame)
gene_list <- c("124511", "124512", "124513")

#create empty vector to collect input
list_collection <- NULL

#loop
for(gene in 1:length(gene_list)){

  #Select genes one by one
  geneid <- gene_list[gene]

  #Your code 
  fetch <- efetch(geneid, db="protein", rettype = 'gp', retmode = "text")
  rec <- gbRecord(fetch)
  seq <- getSequence((ft(rec)))
  m <- as.data.frame(seq)
  setnames(m, "x", "sequence")
  protienName <- names(seq)
  m <- add_column(m, protienName, .after = 0)
  m$molecularweight <- mw(m$sequence)
  m$m<- str_count(m$sequence, 'm')
  m$cc <- str_count(m$sequence, 'cc')
  logvec <- grepl('(Protein)|(Region)', m$protienName)
  m <- subset(m, logvec)

  #Add unique gene to the first column for downstream filtering 
  m <- data.frame(geneid, m) 

  #Collect information by row without re-writing 
  list_collection <- rbind(list_collection, m)
}

Maybe you can use dplyr::mutate, it can add new variables and preserve existing.