The mentioned iMacros is a good option. Create a .csv file with the login info and proxies and specify that as datasource. Name the datasource file to accounts.csv and put it in the root of your c: drive (you can give different filename/route, but you need to modify the datasource route in the macro accordingly), put one instagram account in each line like this:
[TABLE="width: 900"]
[TR]
[TD]COLUMN 1[/TD]
[TD]COLUMN 2[/TD]
[TD]COLUMN 3[/TD]
[TD]COLUMN 4[/TD]
[TD]COLUMN 5[/TD]
[TD]COLUMN 6[/TD]
[/TR]
[TR]
[TD]instagram username[/TD]
[TD]instagram password[/TD]
[TD]proxy ip address[/TD]
[TD]proxy port[/TD]
[TD]proxy username[/TD]
[TD]proxy password[/TD]
[/TR]
[/TABLE]
The macro:
HTML:
TAB T=1
TAB CLOSEALLOTHERS
SET !DATASOURCE c:\accounts.csv
SET !LOOP 1
SET !DATASOURCE_LINE {{!LOOP}}
CLEAR
PROXY ADDRESS={{!COL3}}:{{!COL4}}
SET !ENCRYPTION NO
ONLOGIN USER={{!COL5}} PASSWORD={{!COL6}}
URL GOTO=https://www.instagram.com/
TAG POS=1 TYPE=INPUT:TEXT FORM=NAME:NoFormName ATTR=NAME:username CONTENT={{!COL1}}
SET !ENCRYPTION NO
TAG POS=1 TYPE=INPUT:PASSWORD FORM=NAME:NoFormName ATTR=NAME:password CONTENT={{!COL2}}
TAG POS=1 TYPE=BUTTON FORM=NAME:NoFormName ATTR=TXT:Log<SP>in
PAUSE
CLEAR
Play this in loop. I added the PAUSE command at the end, because i'm not sure what's your endgame. It also sports the CLEAR command, which clear all browser cookies/cache between two logins. This is for the web version of ig, but if you want to login to iconosquare or webstagram or any other ig web viewer, you can change the login process part of the macro according to that. If you don't want to loop through all of your ig accs, just specific ones, you can alter the 'SET !LOOP 1' line of the macro, e.g. if you want to login to the account which is in the 33th line of your .csv, change that line to 'SET !LOOP 33' and so on.
If you don't want to use iMacros for any reason, you can use the FoxyProxy browser addon to configure and switch between proxies with ease. But this way, you can easily login to accounts with the wrong proxy, if you forget to switch between them and you manually have to clean the cookies each time.