The duo are the first Robins players to agree to join Guernsey FC since the clubs agreed a partnership deal earlier this week.
They are in Guernsey's squad for the trip to Herne Bay in Isthmian League Division One South.
If the pair play they will become the first non-Guernsey players to feature for the Green Lions.
"We're delighted to help Guernsey by sending Jake and Kodi to them for a month," Bristol City director of youth recruitment Brian Tinnion told the Guernsey FC website.
"This forms part of our plans for a bigger partnership with Guernsey. Working with their manager Tony Vance, we're looking to only extend this over time.
"We're already looking at the possibility of a pre-season friendly in Guernsey, potentially with the first team, or a Select XI including our under-23s."

The incidents, which occurred overnight between Sunday and Monday, took place in Granton, Boswall, Trinity and Hawthornvale.
The cars targeted all had their windows smashed or had attempts made to smash them.
About 25 incidents have been reported to police, however there may have been other vehicles damaged.
Due to the number of incidents and the scale of the damage, officers are treating the incidents as linked and are appealing for witnesses to come forward.
Insp Shane McKenna, of Drylaw Police Station, said: "This is an appalling number of vandalisms and the sheer scale of the damage caused is completely unacceptable.
"Not only has a lot of damage and inconvenience been caused to a large number of people, it has also caused a number of police resources in the north of Edinburgh to be diverted in order to investigate.
"We are eager to trace those responsible as soon as possible. We would ask that anyone who was in the north Edinburgh area on the evening of Sunday, November 13, and saw this damage take place, to get in touch with us at their earliest convenience."
Guernsey FC have signed Bristol City forward Jake Andrews and defender Kodi Lyons-Foster on month-long youth loans.
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Police in Edinburgh are investigating after 25 cars were vandalised in one night across the north of the city.